1 - There are no "Catholics" yet, the world of mainstream Christianity has not split into Catholic and Orthodox branches yet, although the distinction between Easterna dnWestern already exists.. The Uties (my shorthand for Up-Timers) are all simply "Christians". They'll come up with something to replace the Bishop of Rome. And this Christianity/Catholicism will evolve very differently to OTL, being unrecognisable inside a century or two. Looking at the Emperor at this time - Henry IV - I can very much imagine him appointing his own Pope. I won't even go into what is happening and will happen - or not - in Palestine ...
2 - there will be no Crusade as the concept has not been invented yet.
3 - there will be a meat grinder along the Gothic Line between the HRE and SPQR. Who will win? IMO a toss up.
4 - I wonder about the internal stability of the HRE. In OTL the struggle between Henry and Gregory was part of the struggle between the Emperor and German aristocracy. Here the aristocrats might turn to Rome - i.e. Tiberius - for aid against Henry. IMO no dearth of potential rebels - in OT the Saxon Rebellion (which Henry had problems putting down) was about to erupt. Fun times!
As the OP was not kind enough as to supply a usable map:
If Czechia - a vassal - IS included (unlike Burgundy), then - in spite of my suspicions - it should stay loyal as in OTL Vratislav backed Henry both against revolting German nobles and Gregory.