I am sorry to say the carrying case for the Kreg R3 does not have room for a clamp.
No. The clamp is extra.
When I got mine it came with a vice grip style clap
1" is enough. The grey porrion of the jig is adjustable to work with different thickness of wood.
To the extent any screw could do it I suppose yes. However, my experience is that screws don't hold well there.
Seems to be normal and I'm not sure it's meant to be removed.
I'm not sure about the side load rating of the screws but if you are building this platform bed for an adult, the load should be resting on at least one load bearing post. The platform itself can be built using the jig and screws then the platform corners should come to rest on top of support beams (at least one) depending on your design. Especially if, as you stated and I'm quoting " I'm a big guy". Hope this helps.
Yes. It's actually perfect for that.
The only other things you need are a drill and a clamp to keep it from moving.
Yes it will but you will need to get special screws for use in MDF.