A bunny really knows how to worry it’s hoomin´.
As for pulling out stitches, it can sometimes be due to pain, so in some cases you need to increase the Metacam dosage. It’s good you’ve been in contact with your vet. And I do agree that letting her out might help her relax and feel “normal”. She shouldn’t run and climb and jump of course, but some light exercise is often beneficial, both for the tummy-function, the mood and the wound-healing.
As for her sleeping with her eyes open, i don’t know if it has to do with the surgery or not, it is however perfectly normal for a bun to sleep with its eyes open. Some buns always sleeps with their eyes open. Rabbits have a transparent third eyelid that prevents the eye from drying out.
The easiest way to check her wound without picking her up is to try and sneak a peek while she’s periscoping for a treat. You should check the site at least once daily.