There is friendly fire in the game. However it is mostly minimal.
The game has no set rules for friendly fire. What deals friendly fire and how much is pretty random. One of the reasons I think is because the game can't distinguish allied units from your own so to prevent teamkilling on purpose, most weapons deal only minor friendly damage.
If you want to, you can take a look at
https://coh2db.com/stats/ to figure out which weapons deal how much friendly fire damage. Select the unit and its weapon system and look for the stat "damage friendly" and compare this to the stat "damage" to give you a rough idea.
For example the Panzerwerfer rockets deal 80 damage per rocket, but only 2 damage to friendlies. Suppression isn't modified so friendly units do take full suppression from the rockets.