I've migrated ISP's once, but this was many years ago (FTTC to FTTC that is).
My experience was that I lost PPP session overnight on the effective date of migration and had to change the login details.
The DSL signal will only drop if the backhaul is being changed, e.g. from BT's WBMC to GEA (effectively LLU using ISP's equipment in the exchange) or such. The DSL signal will also likely drop if the speed limit is being changed, e.g. 80/20 to 40/10.
1) It's probably just a standard message to be safe, you can follow it if you wish but personally I don't see how it would have any effect. I also noticed not long ago that I can use my Zen Internet login on my AAISP connection and vice versa (I have two FTTC connections, one with Zen and one with AAISP, at the moment).
2) Possibly, see above regarding the DSL signal.
3) If it remains on BT backhaul then yes I imagine this will be the case. I think Plusnet use BT backhaul?
Hope this helps.