My question is can I buy production boost in the first 300 ticks out of protection.
Thereby having equal to 2 production boosts running at the same time.
One from the protection trade and one purchased with Red tokens

The production package doesn't need reds, you can use blues for it. And yes you should be able to use it even with the boost of dropping protection.

Yes production boosts will stack, so by buying the extra 200 ticks worth you'll go from 300 ticks of production boost (assuming you exit the shield on tick 1) to 500.

yep, but the production will still only increased 50%, no more. And while it's unknown that u'll stay alive at tick 300, buying the production boost at tick 1 to increase it to 500 tick is not a good move.

I recommend buying it in the last 50 tick, so that u can have a production boost every single tick u're playing without it goes out.