I called to schedule an inspection appointment but I was confused when I was told that I should drop my car for "couple of days" to be inspected and diagnosed. Is that true? or I have misunderstood?

Yeah I left mine for a whole week, but they started on it in 3 days and finished in 1 more day. I had went out of town for a week. Came back and was very pleased

Depends on what the problem is, sometimes it takes a while to figure out what the problem is, especially if it's interment.

I've not had an inspection done, so I don't know how long it takes, but many places are short staffed and it is taking longer for many service requests.