"I took my girlfriend shopping and I made her buy so many things ('there' is not needed)". I made her buy doesn't look good. It seems I forced her to buy those things." Two sentences are required.
Indeed "I made her buy" indicates that you forced her."I got her to buy" is probably the most natural. Also natural is "I convinced her to buy."
"I took her to cinema and I showed her that movie". Is it correct?
No. I took her to the cinema and we saw that movie.
Student or Learner