If so, I admire this game's logic.

If you are required to destroy the buildings (it should tell you in between each stage/level) you will need to find boxes of grenades and later rockets, then use your right mouse button to throw them. Be careful as it's very easy to shoot the boxes and blow everbody up.

Ah, thanks.

Sorry, it's the right button to fire and both buttons to throw grenades or fire rockets.
You can also seperate your team members by clicking on their names and then the symbol above.

I am so dumb, I didn't realise I needed to *find* the grenades first before I could use them, I assumed I started with at least one since there was an icon for it. The grenade icon doesn't have a zero, so I thought it was ready and available but I couldn't activate it.

just posting for dumb users like me who might be struggling with this.

Sometimes you will start with some "heavy weapons"

if you split the squad, you can choose whether they take none (no yellow box around the grenades and bazookas) half (dotted yellow box) or all (solid yellow box) worth knowing :)