How do I root this phone and any risk of losing Ltd for my region?
Check on xda-developers for your device. Search for root in Xperia zL/zQ forum. (Isn't Xperia zQ also known as xperia ZL in other parts?)
Rooting will void your warranty and in very rare cases can also brick your phone. Follow all instruction given very carefully.
Rooting probably will not affect Lte for your region.