I have a pair of these already (says size "10.5") that fits perfectly, and want another. If mine were "wide" would size say "10.5EW"?

I would stay with the wide. Extra wide is exactly that. My son’s foot is extremely wide anytime I can get extra wide I do. If you purchased wide I’d keep it the same if you need more room then go with the extra wide. This is a great shoe.

What is the difference between extra wide and "D(M)" what does that mean?

"D(M)" is medium width (sometimes called "D" width). NOTE: Skechers "Relaxed Fit" means they are wider in the toe box but not in the heel – for people like me who have bunions or hammer toes. So I get the size I used to wear (10.5 M), but since I got bunions and hammer toe, I now wear 10.5 M in the Relaxed fit. That way I don't have to go up to an 11 or 11.5 for the sake of my forefoot while making it too wide for the back of my foot. I hope that make sense.

What exactly does relaxed fit mean? is this a nice way of saying wide?

No, it is not wide. Relaxed fit means it is a ‘slip on’ style shoe, like a loafer. The laces on the shoe are fake and you do not lace or untie them. They are only there for looks. The most comfortable shoe I have ever worn. I recently purchased my second pair.

Can I replace the stretchy laces with regular laces so I can tie them (for a tighter fit)?

You can replace with a regular shoelace. However I am not sure how much more you would be able to tighten the lace. My shoe did not get loose over time. If you only need slightly more than it is worth a try.