No, there's no age cutoff for Germany. The Blue Card (4 year work visa) requires either earning more than the national average for non-technical roles (currently more than €72k per year pre-tax) and for technical roles more than €33k. There is no requirement to show that the company was unable to find an EU Citizen, if the salary numbers are met.

Germany has a job seeker visa through which you can come and search for job in Germany. I think you need atleast 5 years of experience to get that. There are other ways to come as well( like having a job offer). I mentioned this in particular to indicate there is no age cutoff, since by the time you have 5 years of experience you are in your late twenties.

Not if you're a programmer or in what is called a "Mangelberuf" (a job that the country needs and makes lax visa regulations for).