Yes , it's crappy wood, hard to finish, and will give you slivers. Indoor temps and dryness will cause major checking and twisting. Get a glued up interior post or make one out of some good grade KD lumber.
most post caps that are 4 x 4 are really 3.5 x 3.5 some have a adapter to be used with both, in order to know which is which you have to read the caps product descriptions.
3.5 x 3.5
The actual dimensions measure 3.5 in. x 3.5 in. x 54 in.
You can try longer screws...or Glue wedges to 2 sides so the post is square.
Yes. They will custom cut anything at the store
Yup. But you have to use a high-quality primer first. I recommend two coats. Then use good paint (not paint and primer all in one!). There is a big difference between cheap paint and pricy paint. In this case the price is worth it.
I had the same question. The solar ones I bought do not fit over the chamfered top because the screws enter straight. In this case It may be necessary to purchase longer screws and carefully pre-drill horizontal holes to accept them. Even with this approach the 2 sides without screws may be able to "rock" because if they aren't snug enough. Perhaps caulk or glue might address this. Another suggestion I saw was to cut off the chamfered part so the top is dead flat.
Brush on water based polyurethane (non yellowing) For best results, apply, let dry 24 hours, apply 2nd coat, let dry 24 hours, repeat @ least six times, eight would be better.