1. Many horses sold at the big 3yo store sales in Ireland are bought by those who specialise in getting them to the track as a 4yo and selling them on for profit. The Doyles (Monbeg) and Colin Bowe are leaders in this field. They run them in PtPs because it's less competitive and, I think in the case of the Doyles, they don't have a licence to train under rules. These guys are specifically looking for 3yos that will run as 4yos and can go on to run under rules at 4 or 5. Most rules trainers will prefer to start from scratch and will ignore the PtP runs, often preferring a bumper run to start from the proverbial clean sheet.
2. As stated, the only official rating is OR. All ratings are subjective and many professionals have their own set of ratings rather than rely on others' opinions. RPR and Timeform are usually only rolled out when they agree with the view of the poster. At the end of the (NH) season, the UK and Irish handicappers get together and agree a shared mark for horses over a certain rating (150?).
3. By and large, hurdles and chasing ORs are entirely separate. Sometimes a horse has run in a handicap chase before it has had sufficient runs over fences to earn a chase mark although I believe that this is at the discretion of the handicapper. When this is allowed, the hurdles mark is usually used unless there is compelling evidence to suggest otherwise. As time moves on, a chaser can increase his mark over fences but his hurdles mark may stay the same. As long as the period of time isn't excessive, it's quite possible that a 145 chaser can revert to hurdles off 125 if that was his last hurdles mark. I'm fairly sure that the UK and Irish handicappers have a different qualification period for this and it caused some consternation on here last Cheltenham. The Storyteller?