We can't recommend a specific tire, also there are very similar questions already on this site but i will do my best to answer your questions.
First: it is indeed inches, although not all tire are measured that way, it is rather common for MTB tires to be listed as such. Other tires, say road tires are listed in a millimeter* sizing such as 700 x 40*
Secondly: Clearance measurement will be inside the fork/frame triangle, both on the side and the top near the crown of the fork, and between the stays on the rear. It's hard to say from the image but it looks like 2.25" tires would be doable but not much larger, one issue to keep in mind is that if the tire is extremely close to the fork but doesn't rub, it may do so under a big hit or heavy load.
Third: The size limit is decided by two things, inner rim width and frame clearance. It is likely that 2.25" would be acceptable as a 2.1" tire is compatible with inner rim widths from 19 to about 28mm widths. 2.25" falls very near to this, and i would imagine the rims that came on that bike are right around 19mm inner width.
So i wouldn't go any larger than a 2.25" i think it would likely work, but cant tell you for sure without seeing more or knowing more.
Tire choice should be based on you budget, and the type of conditions you most often ride in, whether it be on a trail or tarmac.
I tried to keep this answer short, but their are a lot of more in depth explanations available if you search the site.
Hope this helps