#1
Interval | Name | Note.(In C)
-----------------------------------------------
1 | Unison (root note) | C
b2 | Minor Second | Db
2 | Major Second | D
#2 | Augmented Second | D#
b3 | Minor Third | Eb
3 | Major Third | E
4 | Perfect Fourth | F
#4 | Augmented Fourth | F#
b5 | Diminished Fifth | Gb
5 | Perfect Fifth | G
#5 | Augmented Fifth | G#
b6 | Minor Sixth | Ab
6 | Major Sixth | A
#6 | Augmented Sixth | A#
bb7 | Diminished Seventh | Bbb
b7 | Minor Seventh | Bb
7 | Major Seventh | B
8 | Unison (Octave higher) | C
b9 | Minor Ninth | Db
9 | Major Ninth | D
#9 | Augmented Ninth | D#
------------------------------------------------

Just a quick question: If applying this table to a different key, lets say A, you just make A the unison and go on chromatically from there? And does it matter which note you use, like for the Minor Second, would C# be just as acceptable as Db?
#2
Pretty much yeah, those intervals are the same no matter what key you're in. So, a perfect fifth is 7 semitones be it in G or D or C or A# or whatever.

As for the whole 'should a degree be sharp or flat', the general rule is that you try to have one of each note in your scale. For example, the F major scale. You wouldn't write F G A A# C D E F, you'd write F G A Bb C D E F. Make sense?
sig goes here
#4
As well as the intervals, it's good to be familiar with their inversions.

A general rule is that the sum of the interval and it's inversion

1. Always, always add up to 9,

2. and the quality of the interval changes (major becomes minor and vice versa)

3. The only exception to rule no. 2 is perfect intervals, which always remain perfect.

Eg

C-E is a major 3rd
E-C is a minor 6th

C-G is a perfect fifth
G-C is a perfect fourth