My responses in order: 1. The safest advice is to wait at least 90 days after entering the U.S. before applying for a green card; however, applying for an E-3 visa after getting married to a U.S. citizen involves some risk. If you are in the U.S. and just changing your status to E-3 from H-1B (and not applying for an E-3 visa), then you really don't have to wait the 90 days. 2. Until January 20th, less than 6 months typically although there was variation depending on place of residence. It appears, however, that USCIS is bringing back the in-person interview as part of the marriage-based green card application process and this will slow the process down considerably to what it was before, which was one to two years. 3. Absolutely; the marriage-based route should be much faster.