Q:

What does chord-suffix mean?

I would like to know how to play extended/add chords on the guitar, for example Cadd9 here. I want to systematize chords and draw diagrams of them.

What does "Сadd9" or "С+9" mean? Can chords such as "C+10" or "С-5" exist?
What does "A/C" mean? Can "A/A" or "B/A" exist?

Where can I see diagrams of chords?

A:

Cadd9 is a C major triad with the 9th note from that scale added. C E G D. C+9 is rather a different beast. It has an augmented 5th note, and because it's a 9th, will include the m7 too. Thus C E G# Bb D. Don't be fooled into thinking 'add' and '+' are the same!
C+10 wouldn't make a lot of sense, since usually the affected numbers are 5, 7, 9, 11 13, but would be C E G# E, not sounding any different from a standard C augmented (C+).
The '-' sign usually means 'minor', so -5 can't exist. 
A/C would be an A major chord, with a C as the bass under it. Strange sounding again!. Yes, A/B is used a fair bit, in jazz, and A/C# is just the first inversion of A major, with the third at the bottom.
There are many sites which show 'chord boxes', some more accurate and helpful than others. Have a look at some chord theory, which will help you understand what's in this and other answers, and clear up some of your misunderstandings. We all had (and still have) some ourselves!
Basic formula: start with triad (CEG). For 'add' the commonest one is 9. So add D. Yes, it's 2 as well, but doesn't sound good against the 3 (D again!), or sus 4, using F to replace E.
The '+' augments an interval. Usually P5. So C+ uses C E G#, where G# is aug.5. With a '7' in the chord, if it's major 7, it uses the major 7 note (surprise!) so C E G B. If it's dominant 7, it uses m7, so C E G Bb. If it's m7, it uses min. triad - C Eb G - with m7 of Bb.

