Yes! Many of my clients make this simple update & it makes a huge difference. Square with simple detail. Good luck :)

Absolutely. You can get column wraps and simply encase the current posts.

New 6X6's or box in/wrap same for 6" square. May wish to beef up the porch railing spindles too if they are delicate and turned with detail (can't tell from photo) like, replace with square no detail 2x2's. Please repost photo when you're finished.

How great does this look?

With the larger columns I would remove the railing. It's used to keep people from falling and since your porch is pretty much at ground level it just serves to visually block the porch.

lose the railings. go grover without the railings.