Re' test drives - bought/sold probably fifty odd vehicles and never once been asked/shown/or asked for insurance. It's pretty much one of those things but to be sure you can ask for the buyer to bring an insurance certificate to show cover for other vehicles, bear in mind it will normally be absolute minimum cover ie damage to a third party only *not* your own vehicle.
Some will not want to drive anyway, others may not be interested unless they can drive.
Always set off first, then go to a safe spot, get out with keys if you're concerned and get back in before giving keys back.
Transfers now IME are all done instantly on the phone or for larger amounts you trust each other and make the transfer before collection or you ring bank at collection time in front of seller and ask them to make the transfer, The buyer can then check online banking or ring their bank to confirm receipt. This is as safe as it can be.
I would not get involved with cash or paper payment (banker's drafts, BS cheques etc).
Before doing this and presuming a gap between viewing/agreement to buy and collection then a deposit is transferred and this being received will confirm all details are correct.
Obviously in general check out the buyer during the initial phone call - again IME buying/selling Cali's the serious buyers know what they are buying and will come across as such, use your judgement and expect a couple to turn up excited - if three blokes in a battered old van then be aware!