As of Patch 2.7 (released October 23, 2014), all damage and health numbers were multiplied by 10, to allow for more fine-tuning of damage numbers, which is why my numbers will be so different from the ones of the other answer currently present.
The Solar Drill always has 12,000 health, but the amount of health a Turret has varies between individual turrets. Generally, a front turret will have 7,650 health, and a back turret will have 11,900 health. Exceptions are as follows.
Sorona - front bottom: 5,300 health
AI Station 404 - front: 10,200 health
AI Station 404 - back bottom: 7,650 health
Note that unlike the health bars of 'Nauts, the health bars for turrets and drills always have 14 blocks when full, no matter what their max health is, so you can't figure out absolute values from that.
Update: The 1.03 patch for the PC version has added a new character, Gnaw, who has an attack called Acid Spit which makes it possible to track enemies while they are cloaked (though it doesn't remove the cloak effect itself). If you watch this Youtube video of Bunnymancer playing Gnaw, you'll see him hitting an enemy Leon with Acid Spit and tracking him even though he is cloaked.
Original Answer: No, there is no way to reveal invisible enemy players.
Currently, Leon's Cloaking Skin is the only ability that allows players to become hidden from the opposite team, and the only way to end the effect is for the invisible player to take an action other than moving or jumping.
The invisible Leon will still take damage if hit by attacks, but this will not remove the invisibility.
Best Answer
Many abilities do reduced damage against turrets, as for ones that do not do any I think is very limited. This list should make it easier to test or calculate. http://awesomenauts.wikia.com/wiki/Turret :)