Yes, caster is having the top tube a little behind the bottom one.
Yes: welding the beam in is mo' bettah than bolting it. Weld it at the outboard frame tubes and gusset it, then put strut tubes in because you can. That will make it stiff. Once it's in, it's in. They last a lifetime. Porsche welded them in too, back in the day. If some day you decide you want to try to make an A-arm front suspension, cutting out the beam with an angle grinder will be the least difficult part of that effort.
And also, apropos of butt-welded frame tubes. Turns out that's the correct way to do that (assuming you can't bend them with a mandrel) so long as your welds are proper.
There's math and everything.