It should "just work"- I have 1.5.1 in my "Applications" folder and 2.0a5 sitting on the desktop at the moment so I don't get confused, but can use both (and have done so, at the same time). Just extract the package where you want it to go. Obviously some code will run in one and not the other, but there shouldn't be anything stopping them running. 

OK, I don't know why sometime old .pde doesn't work in 1.5.1 (but don't really search)…
Can you install this tool :
https://github.com/fjenett/processingjstool 
for 1.5.1 when you have 2.05a or this is another problem ?

Yes, just tested it and it works for me in 1.5.1, although it's a bit fiddly to install- the name of the tool folder has to match the name of the tool .jar, so it has to ProcessingJS (not processingjs or processingJS) or it won't be detected as a tool.