Key Lime Pi asked: Are there certain combinations of types which make for better friendships or romantic relationships? Could a person develop him/herself in new ways by befriending someone of a drastically different type?

No and yes. This is my personal take on this question.
I believe that if two people of any type are mature and well-rounded, they can and will get along well in relationship regardless of how different they are. When it comes to immature people, there will always be problems in a relationship no matter how similar the two people’s types are.
(Because of this belief, I won’t be answering type-specific-ideal-relationship questions. For example: how compatible are ISFPs and ENFJs in a relationship? I’ll leave that to the tumblr idiots).
As to your second question, everyone you associate with has an effect on you. The more mature you are, the less affected you are by negative influences of people around you. If you’re less mature, you’re going to be more affected. Need an example?
Last year I lived with a semi-mature ENTP, mature INFJ, and an immature ESFJ and witnessed the following.
The semi-mature ENTP made quick friends the immature ESFJ and quickly deteriorated in maturity. The ENTP started going to the ESFJ with moral questions, and because the ESFJ didn’t care about morals, would tell the ENTP to do whatever the ESFJ was doing. They both became remarkably like the other. The ENTP became more wild, dated merely for the sexual pleasure, stopped caring about grades (previously a straight A student) etc.
The ESFJ, by association with me (INTJ), started to pick up my dark sense of humour even though at the start, he was quite disturbed by it.
Meanwhile, they left no affect on me. I simply watched as they influenced each other, occasionally pointing it out to them as amusing situations presented themselves.
Because both I and the INFJ were relatively more mature, we had selective influences on each other, but were not affected by the ENTP or ESFJ. The INFJ reminded me to be kind, and I reminded the INFJ not to take feelings so seriously.