Can I flash a ROM of another Android version? I'm currently having Android Lollipop and wanting to flash a Android 6.0 ROM. Would that brick my phone?
Regarding your first question.
In order to flash a rom with higher Android version you need to


make sure the rom is for your device
flash new bootloader
flash new radio 


Note: i recommend upgrading Android version with the OTA update from your OEM (Samsung, HTC, ... etc) because you cannot mess up. And then flashing the rom.

Then follow the usual steps for flashing any rom which are


make sure rom can be flashed on your device
wipe (optionally not including internal storage)
flash rom
flash gapps if not included in rom
reboot


And if you want Root 


find a SuperSU version that your ROM supports
reboot to recovery
flash SuperSU zip
reboot


IMPORTANT : after flashing twrp may ask you to root your device Select NO

Note: you know that a rom can be flashed on your device only if your device's codename is in the name of the zip file. For example : paranoidandroid6.0.1_hammerhead.zip
 Here hammerhead is the device codename , specifically nexus 5.

Make sure to research before doing anything.