Amorphous. The ooze can move through a space as narrow as 1 inch wide without squeezing.
Corrode Metal. Any nonmagical weapon made of metal that hits the ooze corrodes. After dealing damage, the weapon takes a permanent and cumulative −1 penalty to damage rolls. If its penalty drops to −5, the weapon is destroyed. Nonmagical ammunition made of metal that hits the ooze is destroyed after dealing damage.
The ooze can eat through 2-inch-thick, nonmagical metal in 1 round.
False Appearance. While the ooze remains motionless, it is indistinguishable from an oily pool or wet rock.
Pseudopod. Melee Weapon Attack: +3 to hit, reach 5 ft., one target. Hit: 4 (1d6 + 1) bludgeoning damage plus 7 (2d6) acid damage, and if the target is wearing nonmagical metal armor, its armor is partly corroded and takes a permanent and cumulative −1 penalty to the AC it offers. The armor is destroyed if the penalty reduces its AC to 10.
That could be it. It could also be they have expertise in Stealth. Even if expertise is not an option, it doesn't really matter as long as the characters get an appropriate amount of experience points. Besides, the calculation is based on humanoids and a Gray Ooze is not humanoid.
What happens when someone touches the ooze
one question, how do you figure out initiative bonus for monsters?
Can my players make a amour out of it?
Very, very late, but I hope this helps or that someone else has helped you before now, but just so it is out there you use their Dexterity modifier, and add any outside additions like the Alert feat if you would give it to them and otherwise.
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Can I merge with it like a Symbiote?
I would say yes as the "gray" eats metal, but I would say it would be hard to get it in there