Yes, length joins will need scarf joints to avoid large gaps over the seasonal changes that wood undergoes. You need a miter saw and a finish nailer to do this project. A flat 90 edge will get dinged up in no time. using a router to bevel the edge will still give you a modern look without so much damage. Good luck!

Sure, you can do whatever you want. Did you mean like this? You can butt them up against each other, nail and caulk if that's the look you're going for. .And no, I doubt Home depot cuts measured mitered corners, just rough cuts.

All my baseboards are just done with no miter ours are MDF so movement from vlimate is not an issue. There is no way a HD will cut your mitered corners and a miter box ans hand saw work just fine for this if you want to do it.

Yes, all the corners should be mitered for a finished look.

There is really no reason that you have to miter corners. Wood doesn't move that much longitudinally, an 8' pine board will lose less than 1/8" in the drying process and once dry it will not move that much installed in a home. Additionally, remember wood does not react to changes in humidity, it reacts to changes in relative humidity.

A coped joint is really just a butt joint. Mitered corners are popular in woodworking because of glue up. End grain doesn't glue as well as face grain, a mitered angle reduces the end grain and increases the face grain and therefore glues better. It is also the easiest way to handle complicated profiles.

While it is often seen as a sign of superior craftsmanship, it also shows a lack of skill when done poorly. Your walls are probably not going to be true and for someone who is experienced that isn't a problem. For someone who is not experienced it can be a much bigger headache and can look much worse than a butt joint.

I would advise you to go purchase a cheap compound miter saw. You can get one at a big box store for about $100, Harbor Freight for about $80, or a pawn shop for about $40. Play around a bit with the miter joint and see how it looks on your wall, if that doesn't work then try a butt joint and see how it looks.

Be patient when installing and cutting, remember you can cut more off a lot easier than you can add more on. Take your time when you prep them for paint and you will be fine. You are probably not going to get artisan level results but with some patience you can pretty easily achieve better than average results.

Good luck

Miter outside corners only.

Butt joint inside corners, cope if there is a detail.