I've lived in Germany for 7 years and never once have I added a picture to my resume. It's been no trouble in getting interviews and job offers. I work in tech though. So the experience could vary depending on your industry
Generally yes, there was strong demand for software engineers in Berlin pre-covid. It's still there albeit weaker, so you might not find something you want immediately.
As for the visa, there's generally a 3 - 6 month grace period to find a new job that's granted by the immigration office before you lose your status.