The 1st one is indeed m7. Any D>C is a 7th of some sort. Imagine, for a moment, that we're in key D. For the C to be M7, it would need to be C♯. Another criterion is that m7 intervals have 10 semitones between them.

On to the augmented 2nd. F>G♯. F to any G is always a 2nd, of some sort. F♮ to G♮ is called M2. The interval shown is expanded by one semitone, therefore it becomes +2. If the F had been dropped by a semitone instead, and the G was natural, that again would be +2. And - the space between an interval of +2 is 3 semitones. F>F♯, F♯>G, G>G♯. Job done!