Can I flash a ROM of another Android version?

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.