The farm was quite brutal, but perhaps more from disorganization and lack of experience in dealing with the alien buildings. Nothing from first hand experience to learn though.
First of all, like many have already put in the comments: Devastator cannons work for destroying the mission objectives. The marshmallow cubes just had a fair amount of hitpoints on them. Your Vortex mines really should be saved for the re-enforcement teleporters or for wiping out large mobs of enemies like you've been finding.
Shields - you've got lots of people carrying three shields. Share them around if you have anyone running around without any.
Entropy - like Silencer said in the comments, take your equipment off after you've been hit by it. Not before. Also as you finally realised, entropy missile's gimmick is to eat the equipment you are carrying. Including your grenades, which then sets them off. Also I don't recall if you were hit by an entropy missile, but taking your armour off cost you your last two soldiers right at the end.
Random explosions - you were on a mission where some of the re-enforcement pads were spitting out Poppers. Obviously you'd get random explosions.
The smoke clouds were concealing them.
Not being able to see enemies - they've got cloaking devices and there were lots of smoke clouds around. Level the playing field by using them too. With the cloaking devices, even if aliens do seem to be able to see you first, you won't have to go searching far to reveal them. Notice how effective Zombie became at dealing with the cloaked enemies after he started using one.
Finally, when you temporarily drop equipment on the ground so that you can do something with your other hand - don't forget to pick the item back up, You've reduced your firepower on numerous occasions, and in one case you left a Vortex mine on the ground that subsequently blew up and destroyed your shields.
For other things, your Retaliator has three medium disrupters and is only carrying one shield. You probably should swap them with the Small disrupters on the Annihilator. Better to have the bigger guns on the more protected ship.
Now that you've got plenty of time to use during the week and a fair amount of money is flowing in, you might want to re-organize your manufacturing base and move most of the facilities away from the access lift so that all your agents and techs don't start right next to the lift again. Though your focus is indeed more on the alien dimension now, your bases are still susceptible to attack from those hostile to you.
NKF - finally built a gaming PC in 2020 (though not any of that RGB nonsense). Can now play games up to '89!