Yes
B-flat to C-sharp is an augmented 2nd.
Yes. In music an augmented second is then the second degree is raised by either a sharp or a natural, the interval between A-flat and B natural on a piano is an example.
An augmented third is an interval of five semitones, spanning three note names. An example of an augmented third is C to E sharp, or C flat to E.
E flat consists of 3 flats, B flat, E flat and A flat. E flat to B flat would be a perfect 5th interval as B flat is in E flat major, but because your question was E flat to B, B is a semitone up from B flat, this would mean the interval becomes a semitone larger, and a semitone larger from a perfect interval is augmented. Therefore, the answer to your question is an augmented 5th. Hope this helps :)
augmented 5th, as e flat to b flat is a perfect 5th and b is a semitone above b flat, making the interval augmented
a
E-flat up to B-natural is an augmented 5th.
Major third
A major 3rd would be C, so an augmented 3rd would be C sharp.
Those are both names for the same interval, where the top note is 6 half-steps (semi-tones) away from the bottom. It is also known as a tritone, and is halfway between an octave. If you start on C, the augmented fourth above is F-sharp, and the diminished fifth is G-flat. They sound the same (they are enharmonic).
Major first. (+1)
A C to a G would be a perfect fifth. Because the interval was decreased by 2 half-steps (by sharping the C and flatting the G), the interval C sharp to G flat is a double-diminished 5th.