The top fabric web is simply to keep battery in place in a rollover wreck. The bottom front clamp WILL hold the battery in place tight if it is spaced right. I sometimes use a short piece of 3/4" - 1" X 1.8" aluminum strip from hardware store to make a spacer to lock the battery hard in place. Put it under the plastic front clamp to extend the range of tight there.
That big ground wire coming loose may be loose terminal if using the OEM ones, they are garbage and often twist by hand after tight to cause other issues, change them to the normal bolt on oldschool ones and no problems ever again.
There is zero reason to have a battery loose and flopping around in there, it is far too easy to make them solid bolted down, all it takes is somebody caring enough to do it. I change the size of battery all day long to get good deals and it's easy. One of my Focus cars using a 65 series truck battery now and the other using a side post GM battery at $75 Cheap.
Here's a photo of it. Priceyish duralast terminal from Autozone. The wire coming from the engine/starter? area was cut in half at the end (you can sort of see it in the photo). Idiot mechanic brother came to 'help' as I was carefully removing some insulation from it.
I simply don't trust the hold downs from the part stores and I refuse to drop $100 before I find something that works as a
long term fix. Alum. spacers sounds like a good idea, though.
Honestly, trying to put as little money as I can into the vehicle at this point. It's leaking brake fluid. The driver door doesn't open from outside. The exterior paint is shot with bare metal exposed in some areas. The interior seat handles are broken. The passenger seat backrest refuses to lock in place after a big man sat in it. Fuel vapors leak into the cabin from fuel module from being incorrectly sealed somehow. I even spent $50 on the service tool used to tighten down the cap as much as possible. Now there appears to be a new fuel/spark problem. It better not be the pump from Delphi. I just put the damn thing in last year.
I learned the hard way not to touch the vehicle unless I absolutely have to. Things break off this thing just by looking at it wrong. The car did sit for the better part of 10 years. So a lot of it is my own fault and I'm lucky the main thing I had to replace to get it running is the fuel pump and IAC valve.