I have an H1B visa. SS card says valid for work only with DHS authorization. Can I apply for any job using this?

No, you cannot. You are only eligible to work for the employer who sponsored your H-1B visa. If you work for anyone else, you will violate your H-1B. If you want another job, you may be able to file for a concurrent H-1B with the second employer. But a SS card is not a general authorization for employment.

You can work for your H-1B petitioner. That is the only employer you may lawfully work for.l

As the card states, you need DHS authorization to work. Your H-1B only authorizes work with the employer who filed it.

No because the DHS work authorization in your case is an H1B and that status is employer, job and location specific.