Thunderstone game taking too long (2 players)
The original Thunderstone, while a great game, has a bit of a design flaw in that the 'Militia' you start with are just objectively too bad.  It is honestly a winning strategy to spend literally your entire first 6 turns of the game doing nothing but trashing your militia and then starting up building a deck without them.  If you haven't sort of 'realized' this yet in your strategy, the game can be very slow to start and take a long time for your decks to get powered up.

The expansions to the original Thunderstone address this to some extent by adding ways to kill them off into the monster abilities and some spell/item effects that otherwise utilize them.

Thunderstone Advance makes them better by reducing the XP cost to promote them to a L1 warrior, and adding an equipment to your starting deck that gives an ability when equipped to them.

For the base game, you may consider simply starting with fewer of them in your deck to speed up the early development and be strong enough to start going to the dungeon faster.

1) My group can finish a 4 player game in 45 minutes.

2) Not significantly in my experience, but I rarely play with fewer than 4.

3) Cull some of the militia out of the starting deck.  Use one of the several Apps available that generate 'semi-random' starting boards but make sure things are balanced.  This way you don't get really challenging combinations like monsters that require magic and all figher-type warriors that makes for a very slow start.

4) I always go to the dungeon if I have card draw effects in my hand that give me any reasonable hope of possibly defeating something.  (Not withstanding extreme cases like the Last L3 hero is on top of a hero deck and I have enough gold to get it or something...)

Thunderstone Advance is also a vastly improved game and highly recommended if you are willing to drop more $$$.  Your monsters and equipment/spell cards are 'compatible' and can still be used with it.