Should you remove the lateral shoots if tomato plants are labeled determinate?

I don't. I have tried it a few times. Don't make no difference.
Try a few, and mark them. To see.

Just the first 2 or 3 laterals. Root the laterals, if you have room for more plants.
😎😎😎

No never. Determinate only grows to a certain size plant and stops. Pruning off suckers reduces the amount of fruit you would get from that plant.