Can a skin yeast infection and a bacterial infection occur on the same place at the same time?

Yes: Multimicrobial infections are common. Once the integrity of the skin is diminished, then other organisms can more easily infect the area.

Yes indeed!: An infection on top of another infection is a called a "superinfection" and this is a common occurrence. If the skin is broken down (say, due to eczema), both bacteria and yeast can infect the area, making a real mess of things. Sometimes both oral antibiotics and topical anti-yeast agents are recommended. Dilute apple cider vinegar baths can also help when used with other therapies.