[hdkrgr]

1. They absolutely can and do, but many sell themselves short.

2. Big caveat: There are absolutely many conservative managers who insist on speaking perfect German / not switching the team language because of the new junior dev, so there will definitely be job openings where immigrants are discriminated against at those big corporates, but IME that doesn't apply to the companies as a whole.

The reverse is obviously also true: If you want to work in a young, international, open culture, you might prefer startups, but most of them offer lower salaries.