Best way to apply for position as a teaching assistant
I would omit all the materials in your initial email, and just ask the lecturer a simple concise question:

I would be interested in working as a teaching assistant for your course.  Are there any openings, and if so, what is the procedure to apply?
If not, do you know who I would contact about working as a teaching assistant for another course?

There is no point in attaching your materials until you know that they are wanted and that you are sending them to the right person.