My head cannon on why the Villagers would thank the farmer for:
1. Fixing the community center including the bus, mine carts, bridge etc.
2. Fixing Ginger Island
3. Bringing the Movie Theater into town.

Most villagers do not know that the Junimo are real, but they do know about magic/advanced technology. Besides the Wizard, Emily
mentions the Junimo. She mentions it on Sunday in fall when the farmer has 6 hearts with her. Arthur C. Clarke stated “Any sufficiently advanced technology is indistinguishable from magic”; (Clarke's third law). Magic/advanced technology
can be seen in the lost book Technology Report! regarding Crystalariums. It can also be seen in artifacts such as Dwarf gadget.

The lost book Marriage guide for farmers explains how to geta mermaid pendant from the old mariner; this implies knowledge of mermaids and spirits. The old mariner is a ghost. Abigail, Emily and Willy mention mermaids. Abigail also mentions sea monsters.
Some of the villagers know about monsters. It doesn't seem that big of a leap to think that they would believe in the Junimo when they see other spiritual creatures/items around. They know the farmer is fixing up the community center. They may not know how  the farmer got the community center up and running but they know the farmer is responsible. 

With that in mind, my thoughts are if the farmer can fix the community center than the farmer can also fix the bridge, repair the mine carts, etc.  Given the fact that Robin works super-fast to build buildings and her and Willy can fix a boat up in one night, they would
not be surprised that something was fixed overnight. Marlon knows the farmer is going into the mines and would know that the elevator is getting fixed. He may not know how the elevator is fixed but he knows it's fixed after the farmer shows up. He would also know about the quarry mine. He has to have been the one to put the danger sign up before the bridge broke. As he runs the adventure shop, he would have to know about skull cavern.

The Villagers know the bus works at times; the farmer gets to the Pelican town that way. In my head cannon the bus is like my personal car that used to act up but is easily fixed just expensive. Or maybe the bus has a breathalyzer installed and the farmer pays Pam's fines off and get is removed. Not my head cannon, read it on Reddit but it definitely fits.

Willy knows the Island is in bad shape from taking the farmer there. As Willy takes the farmer there and back, I'm sure they would
talk about how the Island is getting fixed up. Willy may not believe the Parrots fixed it up, but he can see that it is getting fixed. Lewis acknowledges in his (vanilla) resort dialogue that the farmer fixed up the island. Leo would know the island was fixed by the parrots and he has lived with them for a while.