First of all, I would like to thank the developers for making the game free without the usual "give us money to play like a normal person". It's fun, it's not annoying you and it gives you those cool FTL like moments when you need to micro-manage events although on a much smaller scale. I rarely play any games on my phones at all, but now I just can't stop playing the Shelter.
But since this is a request thread, I'd like to contribute a few things I've noticed for now.
The only sort-of-bug I've noticed is that sometimes pregnant women won't be "draggable" at all. Re-launch of the application amends that, but only until the next time it happens again. Other than that, sometimes the game starts to load from the scratch (with vault selection, etc) even though I just minimized the app and opened it 7 seconds later. But that's more of a stability issue which I'm sure will be plenty fixed in upcoming updates.
As for suggestions for future udpates, the biggest one that just gets to me is Energy management. You say that one of the games that influenced you was FTL, so it would be really nice to have similar power management as there. In FTL you could always prioritize your ship's sectors to power off some of the rooms in favour of the more important ones. It's just quite annoying when your power gets below the required minimum and it powers off an entire cafeteria (or just random room) instead of an empty storage room. Also, it seems like there's some kind of cap for Stimpacks and RadAways? So for example you get your 25 of each and then your production just runs on empty. So you can essentially move dwellers to other rooms and power off the unattended ones to save yourself some power. Should be quite handy.
As was mentioned before, maybe some defence options for vault door since now it's just a time delay upgrade.
Oh, and making the map that way that you can only have 3-merged and 2-merged rooms to the right of the elevator is pure punishment
I guess that's it for now and thanks for reading if you're here!