The Argosy comes back after a certain number of quests, I think it's 7-9 or something like that, it's not a fixed amount. You get a message on the loading screen when it's in, as well as the little blue messages shit when you return town. That said, I wouldn't request trade-in items at first. I personally went with materials, and I bought a bunch of annoying specific materials I needed for like random crafting(gathering set needed torrent sacs and some other sacs, I just bought them instead of farming for them for example) and some deliveries. You don't get very rare stuff, but it's nice for when you need like 1 or 2 things but don't want to go farm for them right now. Now he mostly brings garbage though since I outleveled most of the stuff he can bring, so I'll switch him to money(or consumables not sure what that brings).
Also for the tree, you can reuse the same fertilizer before it wears off, and it'll upgrade to the better version even if you haven't unlocked that yet. You just need to do it over 2 quests. It also adds the duration, so it's nice to not have to worry about it too often. Like you fertilize bugs for honey, it'll give 2+2 honey for 3quests. Then do a quest, come back, buy bug fertilizer again. Now it'll give 2+6 for 5turns. It's the same as using the advanced fertilizer, just with more micromanagement, but as long as you hit it before it wears off, it's a lot more economic this way. It's annoying when trying to cultivate different types of things at the same time though, that's where the better fertilizers are much better.