1. You can do a 1031 exchange with the portion of your property that is allocated as investment property (the ADU/rental). The portion of the property that is your primary residence would not be eligible to exchange. However, if you have used it as your primary residence for at least 2 out of the last 5 years, you would be eligible for the Section 121 Universal Exclusion of gain for primary residence of up to $250K for an individual or $500K for a married couple filing jointly. The allocation percentages of primary residence versus investment property would be determined by you and your tax counsel.
2. There is no “2-year clock” in a 1031 exchange unless you are exchanging with a related party. The IRS code does not give specific holding periods to qualify for a 1031 so it is a gray area. Generally a holding period of at least one year is long enough to demonstrate your intent to hold that property as an investment (versus for resale) but it really comes down to what you and your tax counsel are comfortable with.
3. The length of rental periods would not affect a 1031 exchange. If your replacement property is another owner-occupied multi-unit property, again only the portion that is held as investment would be part of the 1031 exchange, while the portion that you live in would be treated as your primary residence.