Answer to question two is yes for Bitcoin and all blockchain like that. There are some new ones like Mina who propose a different system in which you only need

Answer to question two is yes for Bitcoin and all blockchain like that. There are some new ones like Mina who propose a different system in which you only need to verify the last hash. Answer to question three is not restricted to Bitcoin. There are many other systems, e.g. Proof of stake (POS).