Are they the descendents of Jews who arrived in Germany in Roman times, or did they arrive later? If the latter, then when, and from where?

How far back do the latest common ancestors of Sephardic Jews and Ashkenazi Jews go? Where were they located before proto-Ashkenazim and proto-Sephardim went their separate ways?

When did they begin speaking the earliest version of their dialect of High German that would become Yiddish? What did proto-Yiddish replace?