Monster park

1. How do we go in?

You talk to the Monster Park Shuttle NPC in any big town.
You need to exchange 10 ripped ticket pieces for 1 ticket. Ripped ticket pieces can be obtained through monsters.
However, you can choose to buy up to 3 tickets from the NPC Mary which does not require anything at all except your meso.

2. How good is the EXP? Will it be as big of an increase in training speed as LHC was for people 120+?

Monster Park is good, but since your version keeps the party play zones, I think LHC and Ellin Forest will be good EXP for +120.
Tespians can probably answer this question better than me.

How hard are the tickets to find and how long do we get to stay inside once we're in? I'm hoping that they're as easy as that one other ticket event, i.e., every monster drops 'em and it wouldn't take more than 20 minutes (for a good mobbing class) to find 10.

I'm mostly asking for my i/l mage. It's 109/110 right now, and I was hoping monster park would help me get to 120 in a reasonable amount of time while still playing casually.

Thanks for the info, though.