The first is correct. It would be wrong to use 'to' in this sentence. This is because the meaning of the word 'enter', which comes from the Latin word for 'within', already includes the concept of 'into'. Other verbs of movement, such as 'go', 'come', 'walk' and so on, don't include this concept. He walked into the room = He entered the room. NB We do have the phrase, for example, 'to enter into a contract', but this has a specific legal and business meaning: http://www.macmillandictionary.com/dictionary/british/enter-into. When 'enter' is a simple transitive verb meaning 'go into' (a place), you don't use a preposition.

You could also say: You are the first person to enter the room. This sounds more natural than using 'who'.

The first one is correct. "to" is not necessary at all in this situation.