The 757 has been out of production for 16 years, it's just common because it's cost-effective to own and operate for a variety of services.
With respect to type ratings, Airbus shares type ratings between the 330, 340, and 350, but the 340 is basically gone (few operators), and the 320 (their most numerous airframe) is a different type. Boeing has common type ratings for the 777 and 787, as well as for the 757 and 767.
They do. A330/A340/A350 are all on the same type rating. A319/320/321 are on the other Airbus type rating. Boeing has the 737, 747, 757/767 and 777/787 types. Boeing has more type ratings because there is less computerization, all airbus planes fly the same under normal law.
Well, that was weird. A quick Google search doesn't answer it directly but it might be something like:
FAA (and maybe EASA) takes it as 2 types but it only requires a difference training from the 330->350.
From the link: The new regulatory approval means that pilots who are qualified and current on the A330 can already commence their preparations to take the A350 XWB’s controls by undergoing “differences training” only
From what I read the "757-Plus" comments have been widely miss-understood: Boeing is looking at developing a new plane in roughly the same market segment as where the 757 was sitting. They are not looking at restarting the 757 production.
The interim airliner would be an enhanced 767, that is still in production (although not as a passenger aircraft).
With respect to type ratings, Airbus shares type ratings between the 330, 340, and 350, but the 340 is basically gone (few operators), and the 320 (their most numerous airframe) is a different type. Boeing has common type ratings for the 777 and 787, as well as for the 757 and 767.