Is there a computation class describing FOR-programs, what are the limitations?
Having just asked a very similar question:

The language of for programs can express exactly the primitive recursive functions -- see Meyer, A.R., Ritchie, D.M. (1967), The complexity of loop programs, Proc. of the ACM National Meetings, 465.  (I found a copy online here.)

The complexity class for the p.r. functions is called PR.