How fragile is a baby's spine?

Mil and mom comments left me feeling guilty about how I handle my 8 weeks old baby. I do support his head and bottom. But I also hold him under the armpits to lift him up. I also put him in sitting position (while holding him under the armpits so most pressure is not on his bottom) to burp him because it's the only way he would burp.

I also dance with him everyday. I try to move his hand and legs and shake his bottom.

Apparently I'm a terrible mom for doing that and my baby will end up with seriously messed up spine.

Am I exposing my baby to injury? Or are mom and mil just old school?