Grout cracking between ceramic tile
 

I have a small bathroom approx. 12 square feet (3 by 4).
I have some cracking of the grout between some tiles, but not all.
I want to fix those sections where grout is cracking and also want
to re-color the grout to make it look new all-over.
Suggestions appreciated…….

Dig the old grout out and re-grout for a well matched appearance. Small job shouldn’t take long?

You can buy silicone grout that won't crack. I had bathroom floor tiles that were laid down over a hardwood floor, bad move I know. The grout kept cracking so rather than take up the whole floor and do it over I regrouted the cracked areas with silicone grout, that was 5 years ago, and it hasn't cracked since. I also used it where the tile meets the tub because that was an area that constantly cracked, and it's been fine ever since. You wouldn't use it on the whole bathroom, just areas that are prone to cracking.

Start by taking out all the old grout.
You need to make sure the floor is stable, the grout is probably cracking because of a poor install, or poor subfloor. There may not be much you can do about that.
For your situation I'd recommend an epoxy grout, it will be a tiny bit flexible, and much more resilient than a cement based grout. But be careful when installing it, it sets up quick and is a pain to clean up if you don't follow the instructions and watch your timing.
Stay away from any premixed grouts if you want durability.