I'm glad you have a lot to say about my card!
I don't think a Command card playing this is obviously way too powerful. You keep the Command card in play forever. If you wanted a Compost, well, Compost was right there for you to buy. It's true that now you get a Project-like ability where a bunch of cards gained can turn into a Wish. Is it worth sacrificing your Band of Misfits or Overlord for that? I wouldn't call that obvious. If we are really worried about this interaction, it can be an "if you did," as you suggested.
Wishes are extremely powerful, and therefore getting them is difficult and/or limited. And using a Wish is also limited by the "if you did" language on the card itself. Compost itself is also limited by making the Wish effect a one-shot. By contrast, playing a Compost with a Band of Misfits has the potential to give you a Wish effect multiple times from playing a single card; potentially, you could get it at the start of every turn for the rest of the game. Leaving aside self-junkers or junk gainers (Cache, Banquet, Treasure Trove, Beggar, Baron, IGG, Count), this transforms every spare +Buy into 1/3 of a Wish for the rest of the game. I won't list all of the non-terminal +Buy cards, but there are more than enough to make this combination massively overpowered. It is an easy decision to give up a Band of Misfits for this effect. Overlord is somewhat of a more difficult case, but I am almost certainly doing it if there are any of the supporting cards previously mentioned.
I'm pretty sure the Duration effect works. Compost can check if it's been trashed, so at the start of Clean-up, it asks, "Have I been trashed? If I haven't, I've still got work to do." And so it stays out. The effect's duration is from when Compost is played until it gets trashed.
Maybe, but that's not how any official Duration card works. Every single one that stays in play
will do something on the
next turn. I certainly agree that there is one understanding of how Durations work that applies to this card, but I'm nots sure it clearly fits the rules. It is probably okay to say this would be clarified in the FAQ, but I do think at a minimum it needs that clarification.
You are 100% right that if it gets trashed by other means, the cards it's set aside have nowhere to go. I hate Bonfire for being like that, but I'm pretty sure no other card makes that issue arise. My approach has been if Bonfire is the one causing the problem, Bonfire should be the one that gets errata. It causes tracking problems with existing cards as well.
I don't want to put the when-gain-card-set-aside ability on the bottom, because then it can get weird with Ways. Imagine you play this with Way of the Pig or something, and buy a Province. Well, it's not staying in play, but the Province is set aside regardless.
In my opinion, fan created cards should always defer to official cards. However, as you pointed out, Bonfire has some issues with Durations in the official game, and the effect of this one is not to serious, so changing it isn't strictly necessary (especially with your point about Ways).
I understand the concern that this completely nullifies junkers. It does! Compost is not that difficult to put in play. I could get rid of the +Action. That way it will be a lot harder to put into play. How about it?
Getting rid of the +Action helps a bit, but it doesn't really matter if having this card on the board means the junker's are never purchased. Is it worth getting a $5 Moat to force your opponent to play a terminal card every three shuffles? Of course not. There are marginal cases with things like Ambassador (which has a fairly useful non-junking function), but for the most part the cards simply will never get bought, and therefore minor nerf like that won't fix the card.
The only fix I can think of would be to not allow putting a card under Compost if there is already a copy of it under there. This would make it so that each copy only blocked one use of a junker, would make other synergies (e.g. with Banquet or Cache) much less overpowered, and would require a player to forego something besides a Copper and a Curse to get the Wish effect. (It would still be incredibly effective against Looter attacks, but there are few enough of those to not make this totally overpowered, and there is at least one even better defense against those, Way of the Horse).
Edit: By the way, I'm not too convinced that being a flat out counter to junkers makes this card unable to exist. But I will concede if people think it really is too easy and not fun. I mean, on a Compost board, you'll just not get the junker, most likely, and go do something else. And then the other players may or may not want to get a Compost. Then it becomes a question of okay, do I get the junker and hope to play it before people put up their portcullis? There is still some interplay there. I don't want to get Compost early if I can help it.
So, this is all subjective and a matter of opinion, but here is why I disagree. The great thing about Dominion is all of the interesting ways in which the different cards and landscapes interact within each Kingdom to make every game at least a little different. If your card makes an entire category of cards useless, the overall potential for those interesting interactions decreases, rather than increases (unless you think your card is more interesting than all of the official junkers combined). People talk about cards being strictly better or strictly worse than another card. The reason that is important is that if Card A that is strictly worse than Card B, in any Kingdom where they both are present Card A would never be bought, and there are fewer potential interactions. If your card does that with several existing cards, that a substantially bigger problem.
Now, of course, this is a fan card, and (unlike an official card, which could potentially go into a randomizer deck with every other card), it might be fine to design a card that you could just say would never be played with junkers. But since you're submitting it to the contest, and generally one of the criteria on which cards are judged is balance with other cards in the game, I think this is a big problem.
I also think your analysis here is flawed. First, even if you wait until after your opponent buys a junker to buy this, that would mean that the junker would most like only get off one attack before it is rendered useless. Again, that is never going to be worth it with any of the junkers. Moreover, that analysis ignores all of the other reasons to buy Compost. I am opening with this version of Compost in basically 100% of Kingdoms with Cache or Banquet or Skulk or Desperation or Ritual. In any Kingdom where I anticipate getting a +Buy card, I may not open with this, but I certainly would get it early on a $3 hit. As mxdata pointed out, you can easily buy a Copper (or even a Curse, to preemptively weaken the Curser further) with each one, and turning a +Buy into 1/3 of a Wish is, just by itself, stupid powerful. (I also completely agree with their point about Goons.)