Can I omit the preposition "to" in front of every ing-form verb in a series connected by "and"?

Solution 1:

The problem here lies in the depth and complexity of ideas. In your enthusiasm to impress you get unnecessarily complex. Isolating an example:

I (1) look forward (2) to contributing (3) to teaching them.

You could simplify by getting rid of level 2, which adds little to your meaning. The isolated example becomes:

I (1) look forward (2) to teaching [new subjects].

That already sounds much better. How will the whole thing sound with this change?

I look forward to learning new subjects, teaching them, facing new and diverse challenges, and producing outstanding work.

Leaner and meaner.