The answers I got from professional officer:
1. You can transfer H4 with H1, and your expiration dates will be same;
2. You can transfer H1 only, but the H4 expiration date will be different with your new H1, and you may need to renew old H4 before it expires unless (1)you will get Green Card or (2) your family will use EAD or (3) your spouse will leave the US and re-enter the US. Anyway, you will have to renew H4 before it expires (also before new H1 expires) if you want to keep H4.