That looks like a kombucha scoby(symbiotic colony of bacteria and yeast). The taste of the fermented tea is sweet/sour like cider. More info
Some things in your instructions seem off and very conducive to mold formation.
Sufficient acidity is needed to prevent mold. Rinsing the colony in water would dilute the acid.
I would not drink it hot. Most people drink kombucha for it's live bacteria/yeasts. Heating will kill them. Slightly warm on a cold morning is yum though.
Also do not store the culture in the fridge. It is best at room temperature in its own tea.
Air flow is important too. A tight lid on your fermenting vessel would block this A tightly woven cloth or paper towel over the top of the jar held with a rubber band is recommended.
I've been brewing kombucha for over a year and these recommendations come from my experience and a lot of reading that I've done. Kombucha is an acquired taste and becomes addicting.
If you have any questions feel free to ask.