1. I've never been asked for my business card or proof of employment with Avis. Actually, the only time I've actually been asked for employment proof in the travel industry is 1x at a lower-end Marriott property in VA. But as a new renter, never know. I have seen some airports have signs behind the counter for employees noting "these employers/AWD codes require proof of eligibility before departing" but the list is like 6 groups and usually government rates. I really doubt they'd have access to a company database to confirm employment. The only time I've seen something similar is if you book a project rate at a hotel; they ensure you're "on the list" at check-in.
2. No experience here.
3. Yep, but on your first rental, you need to go to the counter to have them swipe your card to associate it to your account, even if you add it online. Or when your card expires or changes, you need to stop to have a physical swipe and comparison of the name on the card to the name on your ID.