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.
The interval between B flat (B♭) and E sharp (E♯) is an augmented fourth or diminished fifth. This is because E♯ is enharmonically equivalent to F, and the distance from B♭ to F spans four diatonic scale degrees. Thus, the interval spans six half steps, which characterizes it as an augmented fourth.
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.
The interval from C to A flat is a minor sixth. In terms of half steps, it spans eight half steps, which is characteristic of a minor sixth interval. This interval can also be described as an augmented fifth when considering the relationship between the notes in a different context.
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).