How to put a picture frame on the floor

I'd use picture wire between the two D-rings to hang the picture. Leave some slack in the wire, as that will give you some scope for adjustment to make sure it can hang level.

Usually, I'd suggest picture hooks, but with insulation in front of the plasterboard, my suggestion would be to drive decent length screws into the studs, leaving the head protruding a little, and hang the picture wire over the screw heads

Based on your description of the loading, I wouldn't be too concerned about supporting it at all unless you're going to leave the framing out for any significant period of time (days for example). If anything it might sag a fraction of an inch, but you'll true it up when the new header goes in. You'll want to remove the old one first and re-frame that section of the wall, then cut in your new rough opening and put the new one in. Pretty simple, and I've done this numerous times with patio doors.

If you're concerned about the weight, consider that there are quite a few houses out there dating from the time before building codes became common that don't have proper headers over windows and doors at all. I've done several jobs where I had to install headers that were missing in the first place. Also, I've done a couple garage demolitions where I had a hard time removing enough structure to make it collapse.