I have a Sears KS-2, which is a rebranded Ricoh XR-7, and had similar issues.
For the meter, try pressing the front "Exposure Indicator Switch" - the long vertical button on the front, just below the red LED. If you've not yet found a manual, here is a link for reference:
Ricoh 35mm camera XR-7 on line manual
www.butkus.org
If that doesn't work, you could do a work-around by firing the first shot with the lens cap on, then hold the Multiple Exposure "ME" lock lever on the back (below the winding lever) so you can cock the shutter by winding but not advancing the film.
Be careful, and don't poke at the shutter. I've had the shutter stick and mirror stay up too. At one point I removed the bottom plate of the camera and found a large amount of lint that I carefully clean out.
However, for me, it turned out the issue was the foam light seals on the back had degraded and a piece got in between the shutter blades. If this is the problem, you may notice your light seals are deteriorating, but it will be very difficult to see where anything may be sticking to the shutter.
It only takes one tiny little sticky piece to cause this issue.
After letting it sit for a few days, try firing the shutter without film to see if it works. Often the foam will release (if this is indeed the issue).
If it turns out to be the foam, the best thing to do is carefully remove the old foam light seals and replace them.
This forum has a number of generic threads on replacing degraded light seals - try the search engine. People have used various replacement foams. I used cotton yarn (from a craft store) carefully tacked into the channels with contact cement - someone also had a thread about this. I used a thick piece of felt to replace the foam at the edge of the door.
I'm not sure about the winding-on issue. Check the bottom of the camera and make sure the "Film Rewind Release" button is not stuck. It disengages the film transport - it should be sticking out when you're taking pictures, and you push it in to rewind. Also make sure the Multiple Exposure "ME" lock is not stuck. You might try "exercising" them a bit. Just fiddle with them for a while and see if they'll move more freely.
There are many versions of the basic camera design in several brands (Ricoh & Sears at least). Some only have auto mode (aperture priority) and no options, but most of the internal components are identical. You can pick them up cheap to use for parts if you need to replace something. Make sure you get compatible parts-cameras, though. Somewhere on the internet is a page cross-referencing them, but unfortunately I lost the link.