Hey Thenp! Welcome to the forum.
Firstly, is there a reason that your including tea in your recipe? I've been brewing for 2+ years and only ever heard of tea being added to turbo cider to provide extra tannins. You should get plenty of tannin from your grain and hop additions in beer so I'd personally recommend scrapping that step if that was the only the reason.
Ideally, you want to limit oxygen exposure too in order to keep the hops fresh and at their best. So opening your fermenter unnecessarily will go against that.
To answer your other question directly, 1.5 - 2.3 vols of CO2 is usually my target for IPA'S, and probably the lower end of that range for a DIPA. That equates to about 50g of table sugar for a 20L batch at room temperature (18c). Fermentation/ambient temperature, the type of sugar, and volume being bottled all play a part though so its probably worth finding a calculator to input your exact figures to avoid bottle bombs - there's a few on the android app store and probably many others too.
If you've got the luxury of a second bucket, then you could transfer the beer to separate the sediment first; but if not, I'd boil a small amount of water and add the sugar to dissolve it, wait for it to cool and then pour gently into the fermenter. Give it a very gentle stir trying to avoid mixing up the sediment and allowing 15-20 minutes for it to re-settle before siphoning off into bottles.