Can I damage my machine if I restart it multiple times? Today I had to restart my rMBP multiple times (2-3 times, one after another) due to a software update, can it damage my machine (logic board, ssd, ram memory) at all? (long/short term)?
Restarting your machine won't damage it physically. The only damage that you can really do to your machine is to the software and/or firmware.  The only way that restarting can do that type of damage is if you restart while operations are still active (i.e. an EFI update or disk activity).  Other than that, you are pretty safe.