Can pubic bone instability cause slight swelling of the pubic mound and groin areas and pain in hip when walking long distances? and sciatica pain?

No: there is no such thing as pubic bone instability.

Shouldn't: While the pelvis is all interconnected, the pubic bone is in the front, and shouldn't cause swelling. It is curious why you think this joint is unstable. You may want to ask you primary care if an imaging study would be appropriate. Sciatica is typically caused by disc disease of the spine. Hope this helps!