When I was eighteen and just started playing the piano, I talked to my somewhat eccentric uncle, who was a fanatic amateur musician. He told me I should write minor chords using lowercase letters. Being impressed by his overwhelming personality, I followed his advice. And it is not a bad idea! It matches the way major and minor keys are sometimes notated in classical music (especially in European countries). For example, a violin concerto would be in D-major or in d-minor. And using uppercase and lowercase matches the way scale degrees are commonly notated.

The suspended fourth is an alteration of a chord, in which the third is moved up to the fourth note (counting from the root of the chord). For example, in Csus4 the third is moved up to the f. In the classical harmony the fourth has to be resolved to the third. In jazz and pop a lot of times this chord will be followed by a regular triad as well. (Though in some styles the sus4 sounds fine as it is.)

In my work as an arranging teacher at the conservatory, I often encounter students claiming that a specific way of notating chords is wrong. Apparently they have learned to write chords in a certain way and they think that is the only correct way. That is a shame, they should have been told that there are a lot of differences in the way people use chord symbols.

In jazz music, a ninth implicates the seventh. Thus, in C9 for example, you should play a seventh as well as the ninth. In this way, time is saved in both writing and reading chords, because most of the time you want to play a ninth in combination with a seventh. If you ever need to notate a chord with a ninth but without a seventh, you write Cadd9. The above knowledge is taught on conservatories throughout the world, and you may find this information as well in theory books and on Wikipedia.