It's a very good idea, and there are lots of things you can do. If you seach YouTube for "office yoga" or "chair yoga" you will find nice videos with exercises that you can do at the office. Some exercises will be more relaxing and some rejuvenating. It's possible to have instructors teach at your place of work as well.
Yes you can do lots of exercises at your desk. You can do neck rolls, arm circles, flex your foot up and down, tummy hold for 20 seconds, and then breathe. Lots more, just think of things you can do.
Some exercises include twisting with your hands folded in towards you (lower back), or rolling your shoulders backwards while holding your hands at your back (upper back).
By holding in your stomach for as long as you can helped stomach muscles tighten. Also, lifting your feet off floor and keeping up for a period of time helps.