I live in Ohio.I have plan to travel in Austin, Texas next week.Can I used my Philippine passport even Iam married now?Can I used it still for my identification ID for travelling to any places of the US?

Yes as long as it is not expired, it is still a valid ID for use.

If I purchase my ticket,Can I used the lastname of my husband or I just used the lastname in my Philippine passport entry when Iam single?