I noticed that Cuban volunteers Maljutka oтделение, would sometimes fire with their personal arms (AKs) at the tank! Instead of using the equipment!
Yes, if you mark tank as priority target - squad will fire with all weapons to it. This is by design.
In this case just remember that this ATGM has a minimum range of 500 meters (near which the rocket does not work - such are the limitations of this weapon), so in the tank with a little distance would not shoot by ATGM.
Also, when I fielded Recoiless rifle, sometimes during very beginning they would "abandon" it, with no explanation (aside from notification that "vehicle is abandoned"
Yes if rocket pool is empty or some crew members is killed and enemies is near - heavy weapons with low mobility is abandoned by crews.
I haven't tested this extensively, but if this is not known bug, I will give more details.
It's not bugs, but normal behavior both in real life and in the game too

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Also, what is present usage of Gaz-66 trucks (aside from transporting troops in tactical battle)? And is there any way to force armored vehicle to stay behind while infantry goes forward? (for instance, attacking AT placement at other side of the hill)
Yes, use of filters (small button on the selection panel), or right-click on any platoon icon on the selection panel (lower-center of screen). You can choose by type of which units are stay selected.
And use groups - Ctrl+number key to save selection, and number key to select.
I can only give great praise to the Graviteam. Its always pleasant to experience a war-game simulation which is not tainted by Western cold war paradigma! Keep up the excellent work and show the world "other side of the coin", with honest research and conclusions.
Thanks!