Yes, augmented chords are a “+”, half diminished aka minor7b5 are notated with that diminished circle and a line through it diagonally.
You can notate chords in lots of ways some times people just notate the tonic and quality like Bb min maj7(Bb minor with a major 7th)
With the Roman numeral system, which I think is the better way to learn chord progressions since its universal across different keys and really let’s you hear the effect of a chord or progressions in terms of how it functions in the key center, the roman numeral signifies the scale degree, so if you’re in C Major a “ii” is D minor or a “biim7” would be a Db minor 7.
It’s kinda difficult to go over all the chord possibilities like a i6 is actually a minor 1 chord with a major 6 because a minor 6th would actually turn it into a major 7 chord. For instance D minor with b6 is D F A Bb, but if you move that Bb to the front its Bb D F A, so it ends up sounding like Bb Maj7. Or with 13 chords, its implied that the 11 is omitted (although all the rules are meant to be broken) so it’s spelled 1 3 5 7 9 13or any combo of those. I’ll try to find a good resource for this stuff and post it. For now, here is the wikipedia page for it, which for the record, wikipedia has a lot of GREAT and thorough articles on music theory.
https://en.m.wikipedia.org/wiki/Roman_numeral_analysis
