If you keep everything bolted up tight it won’t be able to change from where it’s at. To be clear, I’m talking about the bolts from the top of the stand to the lathe bed itself, not the ones from the bottom of the stands to the extra framing.
I can’t really tell what the “framing” is besides the pieces that are bolted to the base. Is there anything the lathe bed is bolted to beside the base? My lathe came with a similar base but I no longer use it since I found the storage in it almost worthless.
Having those pieces at the base could provide additional stability and help prevent the machine tipping over. If you’re concerned that they are causing a problem by all means remove them but I doubt they’re causing the issue you’re concerned with.
The stand is two bases held together by the thick steel plate bolted to either side and there’s almost no way raising it from the ends like that could put enough strain on the center plate to deform it if that’s what you’re worried about. I had mine suspended similarly at one time and it didn’t change the dimensions on the stand or put any extra stress on the lathe bed itself. I also didn’t have any leveling foot pockets besides the ones at the end like yours.
The lathe bed itself is plenty substantial, it’s a bench top machine rather than a larger one with an integrated cast iron base. There’s not meant to be any “support” in the middle of the bed, it sits on the feet at either end. It’ll work the same regardless of whether it’s on the stock stand or a solid bench.
Apologies if I don’t understand what your exact issue is but I’d definitely recommend doing the two collar test. That’s the best way to assess how the machine actually performs.
“Level” really only matters on a lathe to remove taper that can happen when turning long pieces, the lathe can be on any angle as long as the ways are parallel to each other and at right angles to to the headstock and tailstock.
I do have to admit I’ve personally never turned anything long enough for it to matter on my machine which is similar to yours. We have a lot of folks on here with more experience than I do on setting up machines but ultimately what matters is does your setup make parts an accurate as you need.
If you’re new, this may be a case of overthinking the situation. Lots of folks run into the trap of thinking everything needs to be perfect before starting to make stuff. I definitely wouldn’t get into trying to align the headstock before you have a lot more experience measuring and are sure there’s a good reason to do so, too easy to make it worse rather than better.
Highly recommend making some chips soon, it’s definitely way too clean right now
John