I have found these weapon traits in the Tau npc profiles. What exactly do they do mechanics wise?

They should be listed in the armory chapter, no book at hand for page numbers.

Page 143 of the core rulebook, in the armory section.

The weapon never counts as being further than long range, and heavy weapons with this quality reduce the penalty for firing without bracing to -20.

Nuada_Obliage said:

Auto-stabilised is a Trait, allowing the character or creature to move and fire with heavy and automatic weaponry more easily. It can be found on page 130 of the rulebook.

Gyro-stabilised is a weapon quality, reducing the penalties for firing that weapon at long range. It can be found on page 143 of the rulebook.

Mounted is a class of weapon, covering those Heavy Weapons too big and cumbersome to be man-portable, and thus are normally carried on vehicles, fixed emplacements or certain powerful suits of armour, such as Terminator Armour, or the larger Battlesuits used by the Tau. It's been used incorrectly on the various Tau weapons in the Adversaries chapter - a weapon can't be both Basic and Mounted, but rather must be one or the other. It can be found at the top of page 141.