I would advise you to steer clear of the Ortofon 2M Red which I find rather shrill and unbalanced; the 2M Blue is altogether a better cart being more tonally balanced and, of couse, more expensive. The Nagaoka MP110 or MP150 would be a better bet in my opinion and, as you may know, Nagaoka are flavour of the year on these forums. Quite rightly so. If you have to choose between your two listed carts then the Rega Bias.
It depends how much of a discount price. A normal price RP3 comes with a £119 Elys 2 cartridge, which it deserves. It'd have to be less than £400 to make any real saving.
In my opinion, yes. The Bias 2 and 2M Red would both undersell that turntable - in other words, they are designed for cheaper turntables, and you wouldn't get anywhere near the best out of the RP3 with either of them.
The Elys 2 is the cartridge which is designed to go with that turntable (or, at least, designed for that level of turntable) and is a very good fit. I bought this combination a couple of years ago, and have been very happy with it. As I have read many times in this forum, you can get much better results from the RP3 with other cartridges (Nagaoka get a special mention), and I'm planning to upgrade my cartridge soon, but the RP3 / Elys 2 is a very good combination to start with. I've been delighted with it, having been used to cheaper hi-fi (Rega Planar 2 / Bias 2) beforehand. It is a huge step up in sound quality.