Hi Elizabeth, on the song "She Came in Through the Bathroom Window" its generally a Paul composition we know, but who wrote the guitair melody? Does George compose it or does Paul write everything and George just plays it? I suppose this question applies in general to any song by any band... suppose we take a famous Lennon song with a famous instrumental melody, say... In My Life... so theres that famous 6 note guitar melody, does George compose this or John? Also you have that harphischord improv in the middle, who wrote that music, John?
With most Beatles songs, you can use a general rule of thumb of "you wrote it, you play it," but there are obvious exceptions (George and Ringo singing Lennon/McCartney songs, Paul singing parts of "A Hard Day's Night" and "Day Tripper" that were too high for John to sing).
Even when they weren't credited as a songwriter, they still contributed to a song's creation. For example, Paul wrote the lead guitar solo he played on "Taxman," and George wrote the acoustic four-note riff that goes throughout "And I Love Her."
"She Came in through the Bathroom Window" is a tricky one because there actually isn't a consensus as to who's playing which part! There are some that insist that George is on bass and Paul's on lead guitar. But in my personal opinion, that solo is George through and through.
I'd also take an educated guess that George came up with the intro to "In My Life," too. And that sped-up piano solo in the middle? That was completely written by the man who played it - George Martin.