Kitchen faucets are typically 8" c.c. (center of left inlet to center of right inlet). Bathroom lavatory faucets are typically 4" c.c. Although there are 8" lavatory faucets, they are typically only found in residential bathrooms. Single handle faucets follow the same rule of thumb, but once in a while you'll see a single-hole single-handle faucet.
You can pick up a faucet that will match your existing faucet at any hardware store (including the big boxes), but it's not a bad idea to look underneath the sink to check the number & spacing of the holes before you go shopping. And yes, you can change from a double to a single handled faucet (or vise-verse) provided the new faucet matches the number and spacing of the holes in the sink or countertop.
Hope this helps!