Should I repair the kraft paper vapor barrier after remodeling work?
Yes, you should repair or replace the vapor barrier, depending on your climate. In most areas it's important to prevent moisture due to human activity from reaching the frost front inside the insulation, where it will condense and cause mold or damage. 
Yes, you should use faced batts as replacements, unless you intend to install poly sheeting over those cavities instead.
Yes, it may make sense to simply blow in cellulose or fiberglass over a new vapor barrier, but we can't say with the limited information provided. (Cost questions are also generally off-topic.)
Minor debris is inconsequential, except where it's large or heavy enough to cause compression of the insulation medium.