What are all of the signature tags?
Are they just the same as all of the HTML tags?
Signatures in mybb?
Yes, I think I have found them after doing a bit of "research", and I found this link: http://docs.mybb.com/1.6/MyCode/

Mostly what I was looking for was the [img] tag.

EDIT: What size do you recommend signatures to be?
About the size you have now is "standard" mainly nothing over 150 (200max) pixels in height should be ok on most boards. I usually made mine 450x150 rather than 600 though...

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