1. After a successful run, which cards does the runner get to access? All vertically oriented cards for a remote server, and all upgrades plus top of RD, 1 random from HQ, and all of archives for root server? I kept rereading that section and it talked about the appropriate way to pillage R&D, but not when I do and when I don't get to pillage R&D. Maybe it never happens without help from card text, maybe it happens only on root, maybe it always happens (it didn't seem to happen with the remote server in the example though.)
All cards in Archives plus any upgrades installed in the root. Technically, the runner flips all cards in archives face-up and then chooses which cards to access, one at a time. But this only matters in edge cases.
The top card in R&D plus any upgrades in the root. There are a lot of cards that let you access more cards from R&D, and in that case you take from the top and keep them in order.
A random card (or cards, in case you're accessing more than one) from HQ plus any upgrades in the root.
All installed cards in a remote server.
For all of the above except R&D, you can access cards in any order you like. (In R&D I think you must access cards from top to bottom, but you could for example access the top card, then access any upgrades, then access the second card in R&D if you really wanted to.)
However, before you can access cards you must 1) pass all ice protecting the server and 2) give the corp a final chance to rez cards. There are some cards (upgrades, assets) that the corp may rez and resolve after you've passed all the ice that will make your life more difficult.
2. Can the corporation install upgrade cards into a remote server that has no agenda or <decoyagenda>, can't remember the word for the decoy agendas. If you can, is it still considered empty?
Namely, I'm confused as to whether you can install an upgrade on a remote server, and try to fool the runner into thinking that the facedown, vertically oriented upgrade is an agenda.
You can install upgrades, assets, and agendas in remote servers. A server may only have 1 asset or agenda at any given time, but there are no limits on the number of upgrades (exception: you may only have 1 region upgrade in a server at a time). If there is one face-down card in a remote server, it could be any of the above. If a second card is installed in a remote, at least one of them must be an upgrade. You can install an upgrade even if there is no asset or agenda in the server.
A server is not considered empty if there is anything installed
in it. I cannot remember whether a server is considered empty when there is nothing installed in the server but there is ice
protecting it. Not sure if there are any cards that has bearing on.
But yes, upgrades can masquerade as agendas. However, most upgrades (I believe all currently printed ones) cannot be advanced.