Oh, I forgot to answer your other question. If you really want to replace the gravel, then I would probably take the fish out. Just because the water may get gunky, and your sloshing around in there would probably stress him out. There are 2 ways that you could do it.
1) Take your fish out and put him in a container with water from the tank. Take all plants/decor. out and use your fingers to fish out as much as you can, then just pour in the replacement gravel.
2) The less messy approach would be to put the fish into a container of tank water, then siphon out about 75% of the tank water into a bucket, making sure to siphon from near the top of the water as to not catch any debris. Take your plants out and put them in this bucket. Then you can siphon the bottom water, stirring up the debris and sucking it out to partially clean the gravel. Once you have all the water out you can scoop the wet gravel out with a cup, getting it all out of the bottom of the tank. Then, just put the new gravel in (after rinsing it of course) pour the bucket of tank water back into the tank, and replant whatever plants you want to keep. Top off the tank with new water as you would do during a water change, and pour your fish back in. This method would also allow you to really scrub the tank of all algae.
Because your filter will still be on, I wouldn't be too worried about loosing the bacteria, but if you wish you can take some of the old gravel (making sure it stays wet) put it in a nylon bag and put it on the bottom of the tank for a while.
Also, I would catch your betta with a cup, not a net, to avoid breaking any fins which could become infected.
I did a similar thing when I moved my 10 gal. out of my brother's room and into mine (to save the fish!) and everything went well, so this all comes from experience. Good luck.