Hello

I give a level dessertspoonful a day for a robo and I would give the same for a Russian dwarf hamster. So yes it's slightly less than a tablespoonful. A dessertspoonful is the normal spoon you eat cereal with for example. It's probably the equivalent of the two teaspoonfuls Elusive mentions, although teaspoons can vary in size! (And so can dessertspoons I guess but they are mostly a standard size).
The food won't go stale - dried hamster mix lasts for a very long time - which is one reason not to remove their hoard regularly

. They tend to hoard most of the food from their bowl and snack from their hoards and their hoards help them feel secure. So unless the hoard is pee'd on you can leave it for a very long time, then eventually spot clean out the bottom half of the hoard (the oldest food) from underneath, if it starts to get very large. I leave it a few months though usually.
The main reason to freeze hamster food though, is to prevent moths or other bugs hatching out from the food. Freezing the food for a week kills moth eggs and sadly nearly all pet foods contain moth eggs - they are too small to see. I've had a moth outbreak before and it's not nice! It's usually in warm weather they can hatch out.
Once the food has been in the freezer for a week, and defrosted, it is still dry and keeps in the bag for ages. It's a good idea to get a second bag of food before the first one runs out, so you you can put the second bag in the freezer and have it ready when the first one runs out.
You'll need to put new food out in the bowl every day, even if it doesn't all get taken. That might seem a waste of food, when most of it is hoarded, but a bag of hamster food lasts a long time and it's not that expensive - and it helps the hamster feel secure. They like to forage for new food every day and they tend to ignore any food in the bowl that isn't freshly put out (they seem to know!). So it's still important to put some out every day
It would be lovely to see a photo of your hamster! Which hamster mix are you using?