The New Beetles do not get great fuel economy.
The best EPA rating for the 2002 is 28 MPG, my 2003 Convertible is rated at 26 MPG. I doubt you could ever get 30 MPG in anything other than a Diesel bug?
These cars have thermostats, they all fail soft, likely you need to replace yours. These cars have NO gauges other than speedo, tach and fuel gauge. They wanted to go retro like the original bug, they did not even have a tach! You need a scan tool that can display real time data in order to see the engine temp. Engine should run 205-210F. The upper side before the fans kick on usually in traffic.
The blue temp light comes on at cold start, this is normal. Expect the blue light to stay on for approximately the first mile of driving depending on the outside temperature.
Suggest you read the links below in my signature.
As for the turn signals, not sure I would take it to the dealer unless you have deep pockets, find a really good indy.
But first suggest you check the bulbs, bulb sockets and wiring. Might be the turn signal switch.
As for the wipers, check to see if you have the round rain sensor above the rear view mirror. If you the rain sensor, in intermittent mode the wipers follow the rain sensor for the most part. On the other 2 speeds, the wipers should hold their speed.
If you did not get an owners manual, search around and find one online and read up. Not sure if VW has online owners manuals?? Otherwise ebay and purchase one.
Also pop the top cover off the battery and check the fuse box on top of the battery. Many of these fuse boxed melt down due to loose terminals.