Here you must include the “to” in order for the sentence to be grammatically correct. As a general rule, whenever a verb is directly following another verb, it will be in the infinitive form. The first verb in your sentence is “is.”
I want to go to the parade.
She runs to stay in shape.
However, there are some situations where a “bare ...
You teach someone to do something.
He is teaching you to speak English.
to here refers to a purpose, a reason.
If you teach something, you can say:
I teach English.
I teach sailing. [the activity of sailing a boat]
I am teaching them to speak English.
However, we would not say: I am teaching speaking unless it refers to public speaking, the activity.
For what I assume is the intended sense, OP's example #1 is the most natural alternative:
1) I teach you [how] to speak English
But the second version doesn't have that meaning:
2) I teach you speaking English.
In principle that could make sense if we interpret it as meaning I speak in English while teaching you [something, not necessarily how you ...