Should subcontractors have their own insurance?

In the end the general needs to be responsible for all the subs. I would run the subs names through the states database just to make sure

If the GC is hiring the subs then you only need to be concerned about the GC’s General Liability and Disability Insurance and workers compensation insurance.The GC will obtain and maintain the sub-contractor’s insurance. You should request to be added to the insurance policy as an additional insured to protect yourself and your interest.

Yes. Never hire one without it.

Yes,
It is one of those things you never want to need, but you’re glad it’s there if you do.

Absolutely.

Yes! Any contractor must carry Liability insurance & Bond.