First, I think you still ought to have the 'structure' checked out. The Appraiser is not a Home Inspector nor a Structural Engineer. (IF he/she is, they should give more of a 'professional' opinion.) If you've ALREADY been parking your car in the garage, you may be OK in the short term. Over time is when you may have problems.
What you can do for a test is 'string' a line with some sort of weight on it at the CENTER-most point of the beam(s) W/O the car in the garage. The weight, like a pencil, should juuuuuust touch the floor. Then, drive your car in. Now, take a look at your string. If the pencil is resting on the floor more than, say 1/4", have a Home Inspector or Structural Engineer inspect the beam for sure. Don't think that you can monitor this over time because if the beam is sufficiently 'bowed' right now, it could collapse any time!
For what it's worth, the supports (in the casing) were put there for a reason. No one in their right mind would install Lolly Columns to 'take up room' in their basement. I'd be concerned.
As for putting 'treated' wood on the floor to keep 'stuff' from dripping into the basement, I don't think its preventative measure will last too long for the same reasons the floor slightly leaks now. You'll need a serious membrane of some sort to put down, THEN cover with 'something'. I'm thinking of either a very thick sheet of poly or a Snow & Ice Shield type of product, covered with some sort of flooring. (Preferably the latter if nails or screws are gonna be making holes in the membrane.) I really don't have an idea about what the top-most 'layer' might be but maybe someone else on the forum does. DO ask the engineer or the inspector. They should have good ideas.
And thanks for the atta-boy, Keisha and BEG. It's a nice thing. :) We'll keep up the good work. If there's more you need, post up! My best to ya and hope this helps.