Am I entitled to do home office, i.e. to work from home in the current situation?

You are not entitled to work from home, that is, to do "home office". If you want to work from home, you must discuss this with your employer. Many employers are currently making home office regulations. If you get such an offer from your employer, you should take advantage of it. Home office regulations can result from company agreements or a collective agreement. If there is a works council in your company, ask your works council which regulations apply to you. You can find out what a works council is and about its responsibilities here and here.

In some companies, working from home is difficult. If there is no home office regulation in your company, you have to ask your employer whether you can work from home or not.