While you're being vectored, you have to configure for landing, slow down, and run the descent and before landing checklists.
Not really. The descent checklist, if you use one, would've occurred before the vectors...and the pre-landing checklist wouldn't be until around FAF, long after the vectors have stopped. Slowing down in a piston single is not a workload intensive task.
The approach brief should be completed before the FIRST vector. That was my point about being ahead.
As for minutes between vectors as a minimum, it really depends on the terminal environment, but I routinely fly in environment with rapid fire vectors. Having a heading bug helps a lot as you dial it in while reading back and complying with the turn (I haven't used an autopilot during the arrival phase of flight since getting the rating, so I'm aware of the workload of hand flying).
Genna, you're 100% right, it's tough when you're getting started, but you are doing the right thing in going back and asking what you could be doing better, or at an earlier stage of the flight, or more efficiently, and as you said, you now have a better idea of what to expect.
Jordane93 had it right, SPIFR gets you good at managing your time. Ideally speaking, on any given IFR flight, there shouldn't be any particular time when you're trying to do 8 things at once. If so, it's likely that most of them could've been completed earlier when you had 0 things going on. For reference, I'm starting my briefing for an approach at least 40nm from the airport (190kt+ airplane). I rebrief altitudes as needed for altitudes and the missed only.
Tower freq is always dialed in on stdby once I am confident that the radar controller who I'm working with is the last in the chain. A definitive sign is if you hear them handing ppl to the tower, or issuing approach clearances for the airport, but failing that, a proxy would be once you started getting vectored for the approach (although there are times that won't be 100% accurate and you'll still have one more radar controller to deal with). If you're a com1/2 person, you could throw tower and ground on the other radio as part of the approach brief and then swap to it when needed so you don't have to pull from the plate in real time.