Riveos's page

The feat Siege Engineer requires Profession(Siege Engineer) or Knowledge (Engineering), so no, the requirements don't necessarily negate the penalty, though they might.

Kingdom checks aren't skill checks, and on page 199 of Ultimate Campaign in the definition of a kingdom check it says

You cannot take 10 or take 20 on a kingdom check. Kingdom checks automatically fail on a natural 1 and automatically succeed on a natural 20.

I don't see anything mentioning by how much you fail, but I also can't find anywhere that it matters, though I admit to just a cursory check of that.

You're right, total cover = there is literally no space for an arrow to go from point A to point B (without going around, anyway). Since an arrow slit provides a path, however small, that's less than total cover, and Improved Precise Shot ignores it completely.

As for the sniping, sure they can do it, but as you said, good luck with it working often.

Taking 10 and taking 20 isn't included in the Beginner Box rules, but as Ilja says, it's very handy for keeping gameplay moving, if you want to add it to your game. Here's a link to the rule text, for reference.

And Kolokotroni, Disable Device still has that risk in the Beginner Box, so you're right, taking 20 wouldn't apply there.

Actually, Disable Device to open a lock is one of the examples given in the book for using take 20 rules.

Since taking 20 assumes that your character will fail many times before succeeding, your character would automatically incur any penalties for failure before he or she could complete the task (hence why it is generally not allowed with skills that carry such penalties). Common “take 20” skills include Disable Device (when used to open locks), Escape Artist, and Perception (when attempting to find traps)

This becomes even more of a hassle when you remember that constructing a building requires Downtime, meaning that if you aren't directly there overseeing the construction of your castle, then no progress is made without you. You literally need to be there for 33 days to watch the labors make it.

It's actually worse than that, though for different reasons

You must be in the settlement at the start of the construction or recruitment period, but don't have to spend any of your downtime days to begin construction or recruitment. In effect you have to be present only to give the order to begin.

This seems to imply construction doesn't take your downtime days, though it does only specify "to begin". On the other hand, the construction time for each room is additive for the building, so the example castle would take 408 days, or about 13.5 months to build. The gatehouse alone takes 40 days, so even if your GM allows every room to be built concurrently(which isn't provided for by RAW), that would be the minimum, without spending multiples of the Capital required.