Well, tanks are indeed very powerful and basically impervious to firearms and most explosives.... However, they cannot stand up to plasma weapons, and with the machinegun, they've also received susceptibility to laser, so even a lasgun has a chance to damage them, especially from the side. I realize that they're steamrolling weak opponents, but then again, the player worked hard to obtain these tanks...
About the psi, it worked perfectly fine with range limiter, but the devs despite promising me to enable that option, couldn't do that properly and disabled it back. So the Psi will stay OP until I move to the OpenXCom Extended .exe, which now is just a question of time (it allows to make PSI exactly as I wanted it, and offers a ton of new options for a modder anyway, like up to 4 weapons per craft or moddable nightvision ranges); I plan work on the main branch up to Piratez 0.9 and leave it at that, so everyone can enjoy a full "demo" version of Piratez without the need to DL the OXCom Extended, but the updates will only be the coming for the Extended branch from that point on.
So, firstly, I cannot make the tanks to retaliate with the machinegun. Units can only retaliate with the Snap Shot, and I don't want the machinegun to be able to fire single rounds because that'd just look weird (also it's already only using like 25% TUs for Autofire). I could, however, disable the Snap shot of the main cannon (and reduce TU for Aimed shot so you'd still be able to fire thrice in your round), if you feel that reaction fire makes the tanks even more OP. Oh yeah and it seems you've been only using 80% TU Aimed shot on the main cannon, you can use it in the Snap mode too, you know (and with 33% TU, it allows 3 shots per round)
Naturally if you think 3 shots per round are too much as well, we can think about modyfying that too...
Secondly - dw about the lab. It was meant to be unbuildable, that line you saw is a requirement for a non-existing tech. However, I do realize the fact that losing the lab costs you a game; and I can't mod it to be indestructible. I wasn't paying much attention to this, since I've never been shot at with a Blaster and equalled losing the lab with losing the main base, which would be a KO blow anyway... HOWEVER. This is indeed wrong, and there has been something planned from a long time, just not implemented yet: Alchemy Workshop - an alternate poor man's lab, that'd would house only 1 Brainer, unlockable after some research. This would allow you to increase your scientific potential but would require a LOT of space and, what comes with it, money. Therefore in the future versions, after this tech has been researched, the player won't lose by losing the Lab anymore, although it'd still be a severe blow.
About the assault missions I can't do anything, they're harcoded to happen very often after Month 10 of the first year has passed (normally up to 3 times in a month, although once I had to defend the base 4 times in a single month).
Using explosives to defend a base is "on your own risk" action. You're not only risking your buildings, note that you can also accidentally destroy weapons, ammo and other stuff stored at the base. There are other methods of tankhunting too, starting with Molotovs, ending with the usual can-opener, Portable Lascannon (and since latest versions, also MAG Missile for the Missile Launcher). Naturally plasma guns work too but it is hard to obtain them.
Finally I recommend Explosion Height 2, as it seems to give the most realistic blast propagation. When you set it to 3, each vertical tile counts the same as horizontal one for distance, and the tiles obviously have their width smaller than height.