I think the thing is that you installed a 10 speed rear on a bike that was not designed for it. This required spreading the rear to achieve clearance for the wider hub. This has to be done carefully so that the stays are spread the same amount on each side. The fact that your chain rubs on the big ring tells me that your alignment is off. You can check this yourself with the string test, but using the right alignment gauge, like the Park ***-2, works much better. Also, those shift levers were not designed with enough cable pull for a 10s derailleur. Take a look at the Dia-Compe ENE shifters, which will handle up to 11s. The other option is to go with bar end shifters, which will add indexing for you.
Don't get discouraged. A bit of thoughtful effort will get this all sorted out for you. This is the way we all learned.
Edit: I wondered if the Park designation for their Frame Alignment Gauge-2 would get censored. Guess so.