Yes, an engine tune can effect your warranty. See here for a detailed discussion concerning:
http://www.golfmk7.com/forums/showthread.php?t=7492 There are tunes that you can flash back to stock and reset counter; however, if a forensic analysis is performed it could effect warranty claim if it is power train related.
A stage 1 tune is where the Engines Control Unit is modified to increase performance. Tuners change many parameters. Stage 2 is a downpipe allowing for a slightly more aggressive modification of the tune. Stage 3 is downpipe and larger turbocharger.
Rather then changing the software in the ECU a plug and play piggyback device can be installed that will modify the engine inputs being monitored by ECU increasing performance significantly. It can be removed and would not be detected. Here is an example of one:
http://www.golfmk7.com/forums/showthread.php?t=10761
There are many excellent tuners: APR, Revo, Unitronic, Eurodyne, GIAC. Some alow you to do with flash tool, and others you need to go to a dealer. Lots of info in GTI Tune section:
http://www.golfmk7.com/forums/forumdisplay.php?f=28 Some of the manufactures cannot perform tunes on the 2016 models due to changes VW made to the ECU to make it more difficult.
The power plant can handle it and there are a number of discussion concerning. However, the clutch of the manual transmission torque ability to hold is rated below the torque generated by tunes; therefore, a clutch may wear quicker then no tune. You can upgrade the clutch to one that has the ability to match torque of tune.