I leave my car there regularly overnight and have never had issues. The parking garage/train station has security. As others have mentioned, the PD is literally across the street. You should be fine!

Sounds like you've got plenty of good answers here, but just to be clear... the longer you wait the worse it gets. Late fees will be added to the tickets, and if you get booted or towed (either is possible) you'll likely be out $100s more than the original fines. Trust me, the day you get booted will inevitably be the least possible convenient day for you to get booted, they seem to have a sixth sense for that.
If you are able to pay them, you should be able to go online and pay them here. You can also contest them there if you think they were incorrectly imposed. I believe you have a limited window in which to contest them. I have successfully contested tickets before. There is also a link there in the event you cannot afford to pay them and can request a payment plan.

I heard that. I believe Common Grounds is set to take over its spot on Orange as well.

Fair. Yet they were typically quite busy, though if I'm honest if they weren't busy in their respective locations they'd really be screwing up. If anything, the owners picked solid spots for foot traffic.

Literally the highest property tax rate in NH (Claremont) is 40.

The city in CT that I live in now (from NH originally) is 43.8.

It's really not that bad, though with the housing market in NH being what it is, folks are potentially overpaying in that regard (when valuations catch up).