Why did pauper as a play mode die out? Are there any inherent unbalances?
I wasn't there when it did.
Is it realistic to try and practice pauper on normal game modes?
Yes, pauper decks can be really strong actually and should certainly be able to beat people who are using normal to try out their new deck ideas.
What are some of the strong pauper decks/combos?
I'd say GI has some really strong options. They still get their splitters, luccas, drones, scouting missions, infected, CTA's etc. etc.
FD probably loses a lot of tempo, missing their Bromich, Emberstarter, Paladins, Kalis, Klore, etc.
AOE dmg / mill is also powerful I think.
I don't have too much experience with pauper, but I think the above should give some basic ideas for those factions at least.
Any tips for new paupers?
I would say: go to the deckbuilder, filter for only uncommons and later only commons. Then just look for staple cards of the competitive decks. These are staple cards for a reason and most, if not all, should also be solid picks for pauper. Then just look for a common theme / your favorite factions and experiment.
I think you should probably keep it simple too. Just putting characters out every turn to keep tempo up will be a lot less risky than normally is the case. So instead of going for elaborate wombo combos where you need to rely on a synergy of various cards, just start simple I'd say.
Will YOU be participating in the tournament?