Yes, to a certain point. If you have no physical strength worth speaking of, I doubt you can do much more then annoy your opponent. Mentally, definitely. If you have a weak mind you will freeze up.
No. Martial Arts like Jujutsu and Judo, in fact use an opponents strength against him, with little to no effort. I've rolled with people alot stronger than myself, and it all comes down to technique. If you have better technique then someone, strength doesn't mean jack.
I weight about 124, and I'm 5''2, and I protected myself against a man twice my size, and very muscular. It's all about knowing your stuff I guess, and how long/hard you've trained.
Both, just look what happened to Gina Carano she got dominated my Chris Cyborg Santos. It takes a lot of skills and strength. And if your not that song then idk if you would make it because training is the hardest part. But good luck i know you can, just do your best.
If it's a fight with points then all you need is speed and evasive maneuvers.
Being mentally strong is all ninja bullshit put in by movies.
But it's always good being physically strong.