Your analysis is OK, but a bit too general, I think. I feel that 7 Wonders is extremely tactical, making strategy guides less useful. Another big thing is that the game changes a lot depending on the number of players. Nonetheless, it is possible to come up with general guidelines. I'll consider some of what you've written here, then offer some of my own thoughts. Maybe both at once.

As a note, I should mention the "
Complex Strategies" article on BGG. I don't agree with
everything in it, but it is really good.
First, on your points:
1. It's extremely important to get access to at least one of everything, and usually 2 of each brown, 3 if you can swing it. It'll depend on what your wonder is and what cards are important for your strategy. I haven't memorized the card costs so I don't get to take that into account as much when playing IRL, though I did it all the time when I played online here in the forum. Without extra consideration, Stone and Clay are usually more important to get 3 of.
Note that "access" includes neighbours and yellows, and not necessarily what is already on the board. If your neighbours are competent, you can often predict what resources they'll build and give you access to. In one of the games I played on f.ds, I was able to pass on a resource I needed because I knew my neighbour needed it too, and it would be his last chance to get it. I counted on him to build it, and it paid off.
But it can be more general than that. If I'm next to Rhodes or Giza, I can expect them to build more browns than usual. If I'm next to Alexandria and Ephesos, I'll probably have to build more browns of my own. That gives me a sense of what I need to do at the very start of the game, and I'll adjust as the game progresses.
It's also nice to keep track of the resources from the others' points of view. It doesn't always come up, but sometimes you can really hurt opponents by denying them a key resource card. It really hurts Rhodes and Giza if they can't build their final wonder stage. That's also something to keep in mind when playing those wonders yourself -- don't let yourself get locked out.
2. I feel like this is too variable to make a point out of. I've won games with only 0 or 1 resource cards played, but I've also won games where I built enough that I never ever had to buy from a neighbour. The first scenario is probably most likely with Ephesos, where you have good money income even without others paying you. The latter scenario can happen if your neighbours don't have enough resources and can't afford to pay you. It's just so variable though.
3. I have mixed feelings about this point. Generally speaking, I also prefer to play browns and greys in Age I and avoid resources in Age II. However, there are absolutely scenarios where I wouldn't hesistate to play the double resource cards. The most common situations I can think of are in science heavy strategies. The Age I science cards are extremely valuable because of their chaining, but hand distribution means that snagging one might mean skipping an important resource. The browns in Age II can help a lot here.
4. I completely disagree on this point. I will elaborate on this later, but I would say that (in general) you need to get your foot in the door on both Science and Military during Age I, if you plan to pursue them at all. Military could come up late, but that's a thing of opportunity rather than actual strategy.
5. That's something to do in Ages I and and III as well.

6 and 7. These could be incorporated into a larger (and more generally useful) rule of thumb -- consider how much cards are worth to you and how much they are worth to others. Work to maximize your own points while minimizing those of the other players, with focus on whoever is in the lead. If the player to your left is struggling, it's perfectly fine to pass them big blues if they can build them. You can take the card worth more points to you, and they will keep the big blue out of the leader on
their left.
8. Mostly agreed with this. The main thing I would check is if I built more resources than necessary. Related rules of thumb -- you should be discarding for coins as little as possible. I usually consider it a failure if I have to do it more than once in a game. However, sometimes having lots of money is a sign of success... my favourite victory involves Midas, Gamer's Guild and coins out the wazoo.
OK, here are some of my own general thoughts:
ScienceMost of the time, my decision to play Science is based on my wonder. I always consider Science when playing Babylon or one of the grey wonders (in the base game, that would be Ephesos, Halikarnassos and Alexandria). Starting with a grey resource is a big advantage because it lets you get started on Science cards ASAP.
I mentioned above that I feel like you need to commit to Science early. There are two reasons for this. First, every science card you get is a science card that someone else does not. Seems like a tautology, but it's important. The Science strategy is most successful when there is little competition. Playing a Science card early will discourage others from joining in on the race.
Second is because of how Science points accumulate. The BGG article I linked suggests a general principle of point value in each age. While I don't agree with the author's specific tiers, I think the concept is sound. Age II is usually too late to start on Science because they're simply not worth it at that point. One Science set is nice if it's built in Ages 1-2, but pretty bad if built Ages 2-3. If I do start Science in Age 2, it's probably because absolutely nobody else has built any Science and I'm already in a decent position for it (i.e. already have access to all greys on my own or with a Marketplace).
MilitaryPart of this is based on my wonder as well. If my wonder is well-suited to science, I'll put less priority on military cards. If I plan for military to be a significant part of my VP total (e.g. Rhodes), I'll place more emphasis on getting early red cards.
The thing about military is that you do NOT want to get into an arms race with your neighbours. That would be a losing proposition. As with Science, early military plays can discourage neighbours from following suit, letting you win more easily in later ages. You want to play as few military cards as possible while staying ahead. Similarly, it's preferable to play the reds in earlier ages because there is less opportunity cost (e.g. skipping Altar vs. skipping Palace). If you can get a big enough lead early, you don't need to play as much red late. If I know my neighbour will recklessly pursue military victory, it's better to let them have it. -6 is not that bad.
That said, you should watch out for special opportunities, especially after Age I. It can be a strong move to re-take the lead with just one red card, especially late in the age when there's less chance for your neighbour to catch up. This is especially true if you can track where all the red cards are.
So in Age I, my decision is largely based on my wonder/overall game plan, as well as opportunity. In Age II and III, I will play a defensive red early if I'm already in the lead (to discourage neighbours from trying to catch up). If I'm behind, I will usually skip it unless it's late enough that I can get a surprise win.
All of those decisions are also influenced by turn order, as Tables mentions in his post.
BluesIn Age I, the only Blue I want is Baths. If I play one of the others, it's because that hand was really bad. Baths is great because 3VP is good for Age I and it provides a chain to Aqueducts.
Age II is more murky. Aqueduct is awesome but also extremely expensive. 3 Stone is nothing to scoff at. Temple depends on whether anyone needs the chain to afford Pantheon.
Age III is a lot of calculation. Generally speaking, only Gardens is weak, but it all comes down to VP value. In Ages I and II you have to weigh immediate VP against set up for future turns, but Age III is pretty much going for broke. You can figure out how much each card is worth to you or your neighbours pretty easily and pick the best card from that.
Wonder StagesHighly depends on the specific wonders.
Some you want to build early, like Alexandria, Babylon and Rhodes. Rhodes you want early to discourage opponents from joining the race, though it can be hard to do because of how expensive the stages are. Babylon is nice to have early to take advantage of the extra card you get at the end of each age.
Some should be built Age by Age. Halikarnassos is usually best to build on the last turn of each age, so you get the full discard. Giza goes age by age because of opportunity cost -- it's not really worth it to use an Age III card for your first wonder stage.
Ephesos is an "anytime" wonder. There isn't any real pressure to build the wonders early, so it's easy to save them for when you need the money or there is a card in your hand that really needs to be buried.
Olympia is just weird.
