"when do I start making another batch?"

When you harvest the first, unless you want to start one sooner; make as you started the first.

"What do i do with the kombucha culture?"

use it for your second and subsequent batches. You may need to only use a part of the culture and split it between batches to make several gallons at once if you wish.

"Do I only drink the kombucha tea room temp in a glass?"

I do, the day of harvest. I refrigerate the remainder, however, most often I do let it come to room temp before drinking.

"What should it taste like once finish?"

That is personal preference... some like it sweeter, and others like a more tart or vinegar taste. Experiment and find "your" taste.

"Do I need a strainer?"

I have used one and have not used one. More often than not, I will not use one, unless serving someone.