Are the proteolytic enzymes in syconiums and nettles identical to those in rennet?
Rennet is not an enzyme, but rennin is. 

Any protease enzyme should be capable of causing milk to coagulate, or prevent gelatin from setting. Examples such as papain and bromelain are all cysteine proteases, and all of them will cause milk to coagulate. 

The example of fig protease that you mentioned is a cysteine protease (no specific name found, referred to in scientific literature as fig protease). Nettles are a highly polyphyletic group, and the specific enzyme cannot be named without a more specific phylogenetic group being identified.