Hi Wooster, welcome to the crazy world of putting guitars together. Before I get to your specific questions I'm going to make a couple of suggestions
First, get Melvyn Hiscock's book on making your own electric guitar. He is due to have a new one out any day now but there have been many many guitars built from the present one. He will answer many questions you haven't even thought of yet.
Second, this forum isn't the most active for assembling the kind of guitar you are thinking about. Consider going over to the Telecaster discussion forum and lurk (and post) on their DIY subforum. Your questions are asked almost every day - you will find lots of answers
https://www.tdpri.com/forums/tele-home-depot.46/
Your specific questions are a bit difficult to answer without some more information. Have you bought the neck and body? Did you get them from the same source? Is the body drilled for the neck screws? And it sounds like your are using a string thru body bridge with the hole pre drilled.
Assuming that your body is drilled, you just have to trust that they did it right. I can send you a link so you can check the hole spacing. My preference is that the neck not be drilled, what I would do is put the neck in the pocket and clamp it (screw if it is drilled) and yes, check the geometry at this point. Put the bridge in place and check three things
Put a straight edge on each side of the neck and see where it extends over the saddles - it should be over the E string saddles an equal amount on each side. If it is not loosen the strings or clamp and wiggle it until you get it center.
Move the E string saddles as far forward as they will go. Now measure from the face of the nut to the saddle - the break point of the saddle should be at 25.5 inches (the "uncompensated scale length"). You always add some distance to the scale length when you "compensate" for sharpening so you will never need to go farther forward - this will give you the maximum adjustment.
Third thing is to adjust the saddles as low as they will go and lay a 36 inch straight edge on the frets. It should be just touching the tops of the saddle. Again, the argument is that you will never adjust below this point when setting the action and with most bridges you will have adequate adjustment.
If any of those things don't line up correctly it is best to take a picture and post it here (or at TDPRI) and get advice - I'm happy to help with this.
Drilling the bridge thru holes without a drill press is tricky but can be done. My preferred method is to use the plate of the bridge itself - screw it on the top of the guitar and drill the outside holes all the way thru holding the drill as perpendicular as possible. Be very careful of chip out when the bit exits. Drill the other holes half way thru. Take the bridge of and put it on the back, use two drill bits (or wooden dowels) to locate it using the two holes that go thru. Drill the others meeting up with the ones from the top at the mid point. It is much easire with a drill press (pillar drill) - if you can find a wood working friend who can help by all means buy him a pint.
Same thing with the neck screws - if the body is drilled but the neck is not, then clamp is carefully in place (check the geometry per above) and insert a bit that just fits the hole. Tap with a hammer to transfer the centers to the neck . Now drill with the correct size bit for the screw, it will be smaller than the body hole (I'll go out to my shop and look up the sizes). Once again, I find this easier using the drill press but even that is hard because the fretboard isn't flat and wants to rock while you are drilling. I've got some pictures that show this if you confirm that your neck will not be drilled.
Many after market necks come with a nut. They are almost always too tall, but that is better than too short, You can file the slots down as you do the setup. You can also buy preshaped nuts from many of the lutherie supply houses. I simply make my own and can talk your thru it if your supplier does't include one
As far as finish goes, there are as many types of finish as there are guitar builders. Oil finishes are popular because they require no special equipment and are not toxic. Other popular finishes include a gun stock oil called TruOil (its slightly harder than some of the furniture oils) and some people are using wipe on poly finishes from hardware stores. The cardinal rule of any finishing operation is to practice on scrap, ideally of the same wood (maybe your supplier can furnish some scraps).
I'm going to give a couple of links to things I've written - maybe they will help. Here is a scratch built telecaster - you can see the sections on checking geometry and scale, drilling neck holes and some of the other things you ask. Lots of woodworking pictures too
https://www.tdpri.com/threads/a-chamber ... ng.884657/
This is about setting up the guitar but there is a section on nuts
https://www.tdpri.com/threads/basic-setup.952636/
Let me know if I can help further. And whatever you do, enjoy this experience
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