Is English necessary for all German jobs?
It dependents completely on job-type and industry you are working in. For many job-types German only is fine, in "knowledge industry" job fields English is in most cases a must have.
Will I be able to find a job?
Absolutely. The challenge to find a job as UX designer depends on your work experience, portfolio etc. and of course if you personally fit well into the team and "click with the culture" of the company.
All agencies or companies I know are, especially in Berlin, international and even if smaller companies might have just a German team, yet, they will be pretty open to bring someone with good English skills into the team.
This might be not the case for all German cities, but I would not worry at all in Berlin.
