If you don't have the C-ISAM manual, there's an older one online here: http://informixsoftw... Version 50.pdf
Mostly it's aimed at C programmers but bcheck is covered by Appendix A at page 270.
bcheck cannot repair data files, but the structure of C-ISAM data files is trivial provided you are using fixed length records, there is no real sense in which they could be repaired, only restored from your backup!
bcheck also cannot "repair" indexes but what it can do is entirely replace any damaged indexes by rebuilding them from scratch from the data file (if you answer relevant prompts in the affirmative presumably).
I don't think the purpose of bcheck -s is to repair anything, it appears to be to perform some obscure resizing operation within indexes (I have never used it and am merely reading the manual.)
I think the uppercase .IDX thing is purely an "staging" output of bcheck -s where, for some reason, the final step of the resizing requires you to manually replace the 'old' .idx file by renaming the 'new' .IDX as '.idx'
Best I recall, everything is always lowercase .dat and .idx and I don't think you need to worry about uppercase unless you use this obscure -s option and I'm not clear when/why one needs to do that.