Music theory question about intervals?

Both E4 to F4 and B4 to C5 are a 2nd.

THere's no real major of minor in it. The only interval that really matters regarding a minor vs major is the 3rd. That's what determines to our ears about minor or major. So E4 to G4 will be a minor third where as E4 to G#4 is a major third. B4 to D4 minor B4 to D#4 major.

Depending on the key you are in E4 ro F#4 would still be a second but is clearly a whole tone not a half tone rise. So say your in C major (no sharps or flats) you'd play E4 to F4 in the scale, that is a second. But say in G major (one sharp - F#) then in the scale you'd play E4 to F#4 - that is a second too. Any interval is determined by the key you are in (or mode if you want to get really complicated) but still in any scale (or mode) it is the 3rd that determines if it is minor or major.

I hope that helps.

E4-F4 is a minor second, and B4-C5 is a ninth.