I know you cant destroy buildings or planets but can u destroy lasers and cannons and the other defensive structures?

You can destroy buildings and planets (except your original planet) but not defenses or ships. You need someone else to do that

Anything that was build at shipyard can be destroyed, accept for your IPMs.

I hope I am right about IPMs though.

Well you use IPMs to destroy ABMs and defense. Ships can't take out either of them.

sorry I worded that one wrong can other players destroy defensive structures?

as well if I terraform one of my planets does it level all the structures or would everything built still be there?

As I said, any thing that is build from shipyard can be destroyed.
Any adequate attack fleet can destroy any setup of defensive formation. Just the attack fleet has to be stronger than the defense.
After battle the remaining defenses will have 70% chance of recovery.

Defensive structures Destroyable
Rocket Launcher Yes
Light Laser Yes
Heavy Laser Yes
Gauss Cannon Yes
Ion Cannon Yes
Plasma Cannon Yes
Small Shield Domes Yes
Large Shield Domes Yes
Anti-Balastic Missiles Yes (but gets destroyed when Inter Planetary Missiles are attacking, this is a defensives structure for IPMs)

Inter Planetary Missiles No (It is not a defensive structure dont know why it is here, it is an attack system can only be destroyed throw deployment on enemy planet )

all terraformer does is add 4 more build slots to your buildings..so if you have 168 build fields on your home world each upgrade to terraformer would add 4 more build fields..if you used up all your slots you will need to go to buildings click on the structure you want to destroy..option will be at the bottom and that will destroy 1 lvl of that building..say you had lvl 4 storage tank..after the destruction process you would be back to lvl 3

And what indeed would it take to destroy a larger shield structure?

Depending on your Shield techs versus your attacker's techs- a Destroyer will take out a shield.