Hi FranTan. First I'll address your worries about the safety of vaping. Vaping is a comparatively new thing and as such there haven't been any long term (20 year type of thing) studies into the effects simply because it hasn't been around that long. However it is definitely known that the major health effects of smoking are caused by the combustion (burning) of the tobacco leaves (plus some of the additives in cigarettes) rather than the nicotine itself.
There have been a few studies that show potentially harmful substances produced by some types of e-cig but these are in very small amounts, less than the same substances produced by cigarettes. It may put your mind at rest to have a read of some of the articles written by Dr Farsalinos, who is a very respected cardiology specialist.
Secondly, the coughing and itchy mouth. Coughing when vaping can be caused by a number of things. You tend to need to drink more when starting vaping, so keeping a drink to hand to sip can be useful. Also you need to use a different pattern of vaping compared to cigarettes, e.g. with a fag you smoke constantly for 5-10 minutes then stop for an hour or so, with vaping little & often is the rule.
You may want to try reducing the nicotine content of the e-cigs as well. Nicotine strength is a very in-exact science; I was a 30 a day smoker yet happily vaped 18mg, which is normally recommended for people who smoked 20 a day; then again I know other people who used to smoke only 10 a day yet needed the same strength as me to quit with. As the nicotine is absorbed through the mouth rather than the lungs with vaping that could be causing the itching mouth, though as the lozenges work the same way that's unlikely.
You could have a problem with the PG in the liquid, there's a few people on here that had that and I'm sure will post advice.
Lastly do remember that your body will have to get used to not having all the other things that you get with smoking, and it can take quite a while to adjust.