You can stop it over turning by making the horizontal part of the L longer to increase the restoring moment. Other option would be a H shape in plan with the central bar being an upright.As I said to Stu elsewhere I think sliding will be the issue but you can overcome that with plenty of mass!Kudos for motivation.
2. My own board. Probably go for a 50 - which would give me about 3m up climbing height surface. But - how wide can I go if this is partially free standing? Seen them 2.4m wide with no problem - but could I go further (3.6?) but would that make the span of the top a bit long - and possibly a bit bendy. Also quite a lot of weight on the far leg supporting the free end.
I imagine Paul will be along in a sec to say im totally wrong and you'll definitely die, but 3.6m span should be doable. 3.6m is a standard length for timber which is convenient, though I guess you might struggle to maneuver something that big down in to the cellar. My current board only has a single 2x4 across the top 2.4m span, it flexes a little but not enough to be annoying. A doubled up 2x4 should provide plenty of stiffness.
Depends. If you want to reset regularly then use T nuts and yes I think 20cm is standard. If you won't be resetting and want more of a fixed board set up, don't bother with T nuts. Holds with bolt holes can just be screwed on easily with large screws and washers. Saves a lot of initial faff.