First of all, it does not depend on the dialect. Even people from "Schwabenland" (South-West-Germany, ~ Ba-Wü) use "meine Liebe" for addressing their loved ones.
Like @Stephie mentioned it highly depends on the context. But the possesive meine is actually a very strong sign of addressing you like in "my love" (the same ambiguity like in English still applies)
If he wouldn't use "meine" then it the phrase can be related to @runlevel0 answer: When addressing the person you can use "Liebe Frau Mustermann, ich habe eine Frage....". That would just mean "Dear Mrs. Mustermann, ...".
To answer your first question directly, yes, "Meine Liebe" has a pretty strong meaning attached in context of a romantic relationship.
The second question is again relative: There is no such thing like "Seelenpartner" but there is "Seelenverwandter" - a "soul relative" or in proper english a soul mate. Soul mate has the very same meaning in German as in English.
If you would like to answer, again, there is no particular dialect. If you really want to use dialect as a gimmick, than make yourself familiar with https://en.wikipedia.org/wiki/Low_German and I guess you can use http://www.plattdeutsches-woerterbuch.de/pages/plattdeutsches_woerterbuch.html to get some clues of what to say.
Otherwise just stick to "Hochdeutsch" and adress him with "mein Lieber" if it has less meaning for you or with "meine Liebe" if it has more weight for you.