some thoughts only, because it depends:
For the service interval, i´d recommend to check water resistance regularly (each year or two). If moisture gets into the case, you will have a real problem. Most modern movements, which the GP3XXX caliber range is, are likely to require service every 3-5 years. This is much depending on the wearing pattern (how often, how much it is wound when worn) and even weather and environment can play a certain role (deterioration of oil).
Usually and as a rough "over the thumb" rule i´d say don´t fix what isn´t broken. If it doesn´t keep time as accurate any longer or the power reserve is much below what it should have, i´d say it´s due for service.
As for the service work done, i´d rely on someone who is familiar with these pieces and provides a caring service.
Cleaning and oiling should be possible for all qualified watchmakers. I´d say a vital point might not be qualification only, but much more the care and skills that come to play.
On the other hand, sending it to Switzerland might take a while in transit and customs controls.
So, hmm, hard to say.
As for the case refinish, usually this requires to use the same machinery and skills that came to play when the original finish was applied (be it polished, brushed or blasted areas). That´s a really tough call, because personally i do find nothing more disappointing than an apparent "wannabe" polishing job on my watches. It´s so visible when you know how it should look like (and did once), so my recommendation would be to trust someone who really knows what he does and does have the appropiate equipment.
Given both (case and movement need to be reworked), you might consider to send it in to GP Switzerland even if it will need more time than the work done by a regional source.
As to the straps, i´m not sure there´s one which offers the appropiate shape and measurements. To have one custom made might be expensive, though.
As with all these questions and as per forum guidelines, i kindly ask all of your GP fans to provide specific recommendations by email only. Thank you!
Greetings from germany,