You don't need to add 30 days to filing date. It would not hurt at all, just not necessary. Again, if you use date calculator, the 90 day window opens on 01/04/2024, not 01/03/2024.
If you apply on 01/05/2024 or later you'll be bulletproof.
Yes, physical presence requirement is different for 5 year rule and 3 year rule.
For 3 year rule, less presense is required. However, you need to be married and living in marital union for all 3 years. The US citizen needs to be a citizen for at least 3 years also.
Continuous residence requirement is the same for 3 and 5 year rule