Some time ago in my last playthrough I got stuck with some storylines.
Among them Ema. I impregnated her in the beginning, shopped and went to the bar with her in Mohoro, but I couldn't advance the plot with her.
Are there any quests I should complete early to avoid bugs? Any specific quests I should save for last?
well you can messup few quests, as you said shopping with emma you cant inform butthead or you mess up, cant ask about red syringe and such. you can follow guides poped in op for that and i
made one myself for ch2 on things that you can mess up.
but later on not sure how is with early quests you get warnings in chat that you will close paths so that got handy.
i dont think you can save any even if you would want to, since they unlock as your progress, just keep an eye on ingame tracker so you know what you got to do and if you got choices can check the guides. in short, be good to them, whisper on their soul, fuck em when you can, breed them when you can and dont blow them off.
and remember, if you want to invite them to new house, they must have at least 1 kid, not sure if that was changed.