Crossover 6 in. x 6 in. x 54 in. Post Sleeve

Yes, you also need the extra space since the original post may be twisted or warped.

I ordered white and do not remember seeing black as offered. Home Depot would know more about the colors offered.

No that's not the purpose

I had the same issue... but they worked for me. I removed an old fence and was able to get the 4 x 4 posts out of the ground, but had 6 x 6 gate posts that were not cooperating. We decided to leave the two gate posts... cover with post sleeves, put solar caps on them, then hang plant brackets from them. Not yet sure if my wife wants any lattice between them for some kind of climbing vine. But, my point was that the gate posts were 15-20 yrs old and aren't completely straight. The post sleeves are just loose enough to allow for some twisting or bowing so they worked GREAT for us. I bought the 108" length and cut it in half.

Yes you can the paint Dept can help

The only one I can find in searching the website is this adjustable one: https://www.homedepot.com/p/RDI-3-5-in-to-6-5-in-Composite-Fence-Post-Trim-Base-4-Piece-73018131/204727022 . They have one piece ones for 4x4's. They also have a one piece 6x6 for aluminum fencing that might work.

It's about 1/8"...probably 3mm.

This one is solid. You could of course measure carefully and cut an opening for the rails.

No - it's flimsy and cannot stand alone as an end piece.