All of those lines are correct but some don't feel quite right. This morning, or most mornings would be a better choice in a lot of those lines than "in the morning". More on that in a moment.
To say "I took tea" brings to mind a snooty, aristocratic woman telling the hired help that she will take her tea in the drawing room this afternoon, thank you. That's an American's take on it, you may get a totally different response here from a Brit. Viva la differance.
To say the same things, I would choose:
I had tea this morning.
I had a cup of tea this morning.
I have tea in the morning. -OR- I have tea most mornings. -OR- I have tea every morning.
(again) I had tea this morning.
I drank tea this morning. -OR- I drink tea most mornings. -OR- I drink tea every morning.
I drank a cup of tea this morning
In real life, I'm a coffee drinker. :)