Do I need to sign the other forms in an amendment besides 1040-X, for example the original 1040-SR? It has a number for "amount you owe now" which is no longer true.

When you mail in the amended return you do NOT send the old 1040 or the new 1040 only the  signed 1040X plus any other forms/schedules that were changed.  

Look at the form 1040X …

Column A should have the figures from the original return, Column C the corrected figures and Column B the differences between the other 2 which needs an explanation on page 2 of the form 1040X.

If you completed it correctly you will see an entry on either line 16 OR 18:

On line 16 should be the amount you paid with your original return. If you paid nothing already then this line should be zero.

On line 18 should be the amount of your original refund you received.  If you have not received your refund yet then you need to wait for it.  If the refund changes from what you expected then this line must reflect that change.

Then you will see your extra refund on line 22 OR  the new balance due you need to pay on line 20.