The answer to all of those is - it all depends.

Your best bet is to ask at your local 'foreigners office' (extranjeria)

As has been said it really all depends on location in Spain etc and what the requirements are of the local office you will be applying to. As for your ayuntamiento/town hall best again to check if they require residencia to sign on the padron. Realy you should get residencia before padron and my ayuntamiento insist on that now but they didn't 12 months ago. Reason is to sign on padron your Spanish home should be your habitual home and I believe junta are now checking this as the town gets money from them for every resident on padron. However again it's Spain different towns have different requirements.

While I suppose it's not impossible it's difficult to imagine how anyone could claim to be resident in Spain without a Spanish bank A/C, it's so easy to open one as well so why wouldn't you ?

If for no other reason then to maximise your chances of a successful residencia application clearly it makes sense to cover or eliminate any points which could potentially trip you up, amongst those is not being able to demonstrate adequate and regular income in Spain.

Living under the radar is something else of course !

hi adventureboy, bank account yes you do in our area.

5000e we had to have this amount for 6 months

,the bank would not give us certificate need ,only a statement of the account for 6 months this was excepted in our area.
we singed on padron a year before residency,with a signed private sale contract
our town hall are extremely good ,and will help you with anything if they can.
P.S our area is denia oficina de extranjeros
as said it differs area to area confusing to say the least but not as difficult as you might think,good fortune