1: I believe so, though in my game Lona has not gone through a human pregnancy yet. I do think she has gotten pregnant by humans in previous plays, though I did not go past the initial Super Epic Vomit Morning Sickness stage.
2-3: Normally I would say it's not possible for RPG Maker to track data via individual items, especially those that stack. Only eccma417 could tell us for sure. Lona RPG tracks unique enemy and ally data, but aside from changing HP & stamina (which resets on every new map), I see no growth or tracking of special stats. They are reset on new maps.
4: Having babies also gets you milk, and milked. Milk might be good for recipes? Also, being nursed/milked might somehow increase Lona's stats or have some effect on her.. but I don't know yet...?
5-7:
8: Someone complained there was a deadline, but apparently they were referring to the world difficulty. I guess when it reaches 100 then the encounters must get pretty bad. Apparently you can give the church money to reduce world difficulty, though I have no done this yet. I will soon try and seek them out. I believe you can encounter a preacher randomly in the city.
9: There are other trees besides apple trees. You can chop them (even with bare hands, as in Minecraft) for wood but it costs 15 stamina per wood. You can not chop stumps and possibly some trees, but just try other kinds and you'll get some wood. It falls off and must be collected just like the apples. Also, it will be located in your equipment (it is just like the wooden club you started with).
10-11:
12: Someone said you can hold shift (or was it alt?) key while pressing the Q key, and this will make you sleep fully.
I haven't tried this yet as I'm still playing the previous version (no reason for me to update just yet, but that's just me).