Cannot answer all your questions, MajortTom, but I bought a bike there last year and am returning again next month to tour some more!!
I bought a Ronco Demolition - Chinese made - 250cc and it took me 9000 kms round Northern Peru with no problems. My only gripe was that it comes with knobbly tyres and they are noisy on tarmac, and plenty of vibration too. The bike will go all day at 100kph, which is around 6000rpm, with redline at 10000!
The Ronco cost 4500 soles, which is around US$1500 brand new!! Paperwork was a cinch - supposedly you need a permit to sign contracts from Migraciones, but I just went to a notary, they "authenticated" my signature from my passport and that was it. 4 weeks later I had all the documentation in order and new plates on the bike! That gave me time to run it in, and get used to it. You will need to get the compulsory SOAT insurance which varies from place to place - although cover is the same and country-wide I believe that where you buy it makes a huge difference! I paid around US$200 for a year's cover. Some people say you cannot ride without the number plates and/or the tarjeta (credit card sized registration document for the bike) but I carried the bill of sale as proof of purchase and had no problems - and if you look at other new vehicles loads have a sticker saying "plates in post" attached!!
As far as safety round Peru? I, too, had heard horror stories, mainly about police wanting "prata" and finding all sorts of faults with paperwork/bike/etc. but found they were always polite and helpful. Wearing a crash helmet, gloves and a jacket (not leather, but gave me some protection) I didn't look like a rich gringo, and riding a Ronco as well did not bring attention. I had no problems at all, even riding alone, and in remote areas - went as far as Tarapoto in Amazonas. I would be careful in Lima, though (I never went near it as I was based in Trujillo in the North) but again as long as you don't obviously look like a gringo should be reasonably OK.
Can't help with any of the other questions, I'm afraid. I am hoping to tour some more this year - spending another 6 months in Peru - and may even venture South this time!
Have fun and stay safe!