There's plenty of CO2 produced from the priming sugar you kegged with and the yeast still in suspension, which will see you okay to about halfway down the keg.
You'll need to add gas to fill the increased headspace as the beer level drops. The flow from the tap dies down and shortly after the keg starts to 'glug' (you'll know what I mean when it happens)
Just a quick 1 or 2 second blast will be enough.
Finings should have been added prior to kegging, but it's no problem. I only ever used them on my first brew, cleared no quicker than any other.
Plenty more info here 🙂