Do better mons spawn at certain points?

I believe so. Certain spawn points do seem to consistently pump out rares.

Around a year ago before they removed scanners from the game I was in one. That tipped me off to a few places worth checking out that I still to this day occasionally swing by and often find neat stuff at. The most obvious one that comes to mind is right in the ocean along the coastal road. All kinds of crazy rares.

Yes, some spawn points are more likely to spawn rare species. Some time ago they were called "unicorn spots" or something like that due to the rarity of the pokemon you could find there. You're lucky to have one nearby.

Regarding shiny variants I think that there's something similar. But I haven't researched the topic, so I don't know for sure.

I remember a stop would spawn a Snorlax every other week, and met two Blissey at the same spot in a year. I believe stops are not the same and some of them are Niantic-kissed.

It's related to biomes. Sometimes you have a single point that belongs to a different biome and you can find mons rarw to to your usual biome.