'Difference tone' is maybe a term that hasn't travelled well across the Atlantic, but here goes.
Having played an instrument for >3 yrs doesn't mean knowing about intervals! It's maybe not the best criterion. Your prof. really should have explained why E-B is P5, rather than merely telling you. Many, many people who've played for way more than 3 yrs wouldn't know that, and for most of them, there'd be no reason to know, either.
The questions appear to be about intervals, but there really isn't any need to involve any more than simple maths.The reason E>B is P5 is twofold: E F G A B = 5 'steps' (including the 1st). Now why P? P = perfect, and means the two notes are the same - either both ♮, both ♯ or both ♭. Had just either been one of those, the interval would still be 5, but not P5. Still 5, due to E F G A B. That's a cunning plan, only to be spoiled by Bs and Fs...) A safer plan is count the semitones between - P5 always has 7 (without mentioning d6 - oops).
2nd one is, as you both say, M3. Major third. E F G - 3. 4 semitones. By decreasing the space by one semitone, in your case G♯ to G♮, that interval is now m3 - minor third.
Difference tones (also Tartini tones, after Giuseppi, who 'discovered' them) are the pitches heard when two notes are heard - and another note is also apparent. Maths alert! Say one pitch is 1500 Hz, the other 2000Hz. The difference is 500Hz, and were the two notes sufficiently loudly played, a pitch at 500Hz would be heard. Interesting, though - if both notes are part of a harmonic series (i.e. P5, no extra sound will be heard. (Consider Q1). If both pitches are quite close, a different effect will be produced, a sort of warbling, not unlike tremolo, as used by many guitarists when checking tuning.