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.