"I like tea."
At least where I am from, when people say 'tea', it's understood as breakfast tea, which is a black tea blend. However for the sake of learning, you have a point here. It's best to be explicit than ambiguous.
ちゃ should apply here as well since the English sentence doesn't reference to the type of tea.
Not really. が is more accurate when talking about a specifix topic such as you liking tea. If you want to underline general property of tea being delicious you couls say こうちゃは. But the が gives it a more focused meaning.