Nice bike! Do I read that frame right? "Triumph"? and nice yellow paint to boot! A friend of mine has an old 125cc (i think) two stroke thumper triumph.
Manual reccomendations vary from brand to brand but from what I've read and seen on here and elsewhere 32:1 seems to be the standard for two-stroke engines, and its possible to go as lean as 40:1 with synthetic on mopeds. You will want to be careful tho and lean it slowly and see how it does, since your manual recommends so rich a mix, If it's that Haynes manual pictured tho, you are prolly safe going leaner. Any labels on your bike/frame/tank/cap show mix? I don't know your bike, maybe someone that has one can chime in.
Synthetic is only bad during the break in period cause it's _too_ slippery, your bike is probably well broken in so you should be able to switch to synthetic no worries. It also smokes less, as does a leaner pre-mix.
What kind of oil is that comes with a measuring cup?
Also about your low-end, the homeoet is a high-end pipe, http://www.mopedarmy.com/wiki/Puch_Exhausts so it will have power at high rpm when you are already going fast and make you go faster, but the low end on it sucks from what it says here, i don't know if it's worse than stock then it's a trade off, but the carb and intake might help it and balance it out.