Fixed gear bike: when I stop the bike completely I can move the pedals back and forth very slightly is this normal? As the title shows I have a fixed gear bike, not sure if this is right though: even when the chain is tight as possible there will be what seems a loose spot and it makes it so that the pedals move back and forth slightly. For example, doing a track stand I can move the pedals back and forth slightly without moving the wheels, just wondering what might be the problem here, if anyone can help. It’s a Raleigh Falcon BTW so an old bike, that was converted to a fixie.
The chain should not be 'as tight as possible'. There should be some slack. If the chain is over-tensioned you will accelerate wear on it and the sprockets, and increase the possibility of snapping it.

There will be some pedal movement when the rear wheel is prevented from rotating, due to chain slack and the fact that the spaces between the sprocket teeth are larger than the chain rollers.