Yeah, I used a 10 inch wet tile saw for all my cuts. So much easier than an angle grinder.
I'm sure your base is fine for at least a very long time. Eventually it may shift with enough freeze/thaw cycles but I suspect it won't really affect how the oven works.
The Airstream took a lot of work. It required removing the body and reinforcing the frame and installing a new heavy duty torsion axle. It's a lot of fun though, for sure. Also, it's nice cooking in the driveway in the winter when it's too cold and muddy to hang around the backyard oven.
If I'd known I was gonna live this long, I'd have taken better care of myself!