You are good to go with the concrete you have for that type of lift. I can understand the suggestions of cutting out and pouring new thicker pads if it was a 2 post lift but not for the lift you are considering. Use what ever concrete fasteners that are supplied with the lift.
You never place a filter before the pressure switch on a well system. A clogged filter can cause the pressure switch to not achieve cutoff pressure and burn out the well pump. Be sure the filter is after the pressure switch. Pressure tanks can produce rust as they reach end of life so having...
You can use SER cable for the run inside the house and transition to conduit using a junction box switching to XHHW to the garage. The SER doesn't need to be in conduit, it's installed like NM-b.
The original owner had to have it wired as 240v. They just used the wrong outlet and plug and wired as 240v. The neutral of the 5-20 was used as a hot. 240v is two hots whereas 120v is one hot and one neutral so the 5-20 can actually be wired as 240v.