1. Since you are subject to the 10-year ban, you are welcomed to apply.
But you should not expect a lot.
2. I-601 can be only applied when you have officially denied for a visa and you are told you may be eligible.
Addition:
1. Your ban starts when you exits the country. But the date started counting when you were 18 years old.
Even this will reduce your ban from 10 to 3 years, you are still subject to a ban. Even it seems that the ban has been over, it does not mean the U.S. has forgiven your past violation. In fact, many people who have previously subject to a ban are blacklisted for visa.
(The key issue - a nonimmigrant visa application is not subject to judicial review. So even the ban is over, the ban presents a potential risk for future violation.)
2. No. You will have to complete everything in Taiwan (as a waiver is possibly required).