I've never heard your 'nicotine myth' before, either from pro-vapers or anti-vapers. I think you just made it up because you don't know what you are talking about but are having some sort of outraged knee-jerk reaction against vaping. Maybe this is because it looks a bit like smoking, maybe it's because smokers who use ecigs to quit aren't quite miserable enough for your liking. Whatever.
The nicotine in ecigs is pharmaceutical grade - exactly the same as is used in patches, gum, lozenges etc. and which is considered safe enough to prescribe to pregnant women and children as young as 12.
But seeing as you have invited us to share myths, let's make a start, shall we? 
The purpose of this petition.
To place the onus on the e-cigarette industry to fund totally independent research, to prove that their products are not harmful to our health.
Myth 1: Research funded by the ecig industry will be accepted as 'totally independent'
Truth: Some of the best, most useful research for improving the (already rather good) safety of vaping has been crowdfunded by vapers and vape companies (Farsalinos). It is routinely ignored or discounted by the anti-vaping contingent of PH because 'conflicts of interest' i.e. they can't fault the studies so they fall back on ad hominem attacks.
Myth 2: It is possible to prove that anything, anything at all, is not harmful to health.
Truth: That's not how science works. All science can do is look for evidence of harm and either find it or not find it. No evidence of harm has been found for vaping. There are a few small, hypothetical risks which is why the best estimate is ~95% less harmful than smoking.
This is going to take a while! Are you aiming for two myths per sentence all the way through your petition text?