Am I allowed to ask a competitor if they have open positions?

Yes — this is not a breach of contract as long as no valid non-compete clause (Section 74 HGB) is in place. Looking for a job while still employed is completely legal and normal in Germany — notice periods do not prevent this. Caveat: a post-contractual non-compete could apply after leaving, not before. BDSG Section 26: the application data you submit to the competitor is treated confidentially — your current employer is not informed. LinkedIn: most job seekers search discreetly — the 'visible to recruiters only' status on LinkedIn protects you in this process. AGG: discrimination at the competitor is just as prohibited as anywhere else.