Gershomi, to answer your last question, if it is unclear whether a person’s gerus (or their mother’s gerus) was valid, then it is common for the person to undergo a gerus l’chumra to ensure the person is Jewish. It’s just like a normal conversion process (accepting the mitzvos, etc.), except that afterward, the question “are you a ger” is a little complicated. If the original conversion was valid, then you’re not a ger, but if it wasn’t, then you are. Either way, the person has undergone gerus, and that’s nothing to be ashamed of. In terms of whether you have the status of a levite if your father was a levite, I don’t know! But anyway, getting back to “hatafa,” since the person (well in this case a man) was already circumcised, the conversion involves hatafas dam bris instead of a regular circumcision.
It seems fairly common for people with non-Jewish mothers but Jewish fathers to convert halachically. Dov ben Avraham, the author of a recent book on chassidic perspectives on gerim (and author of the A Simple Jew blog), is a ger with a Jewish father. Some rabbis believe that people who are descended from Jews but aren’t Jewish (especially with a Jewish father) should actually be encouraged to convert, or at least accepted without the initial discouragement required of normal converts.
In any event, welcome to the CR, and hatzlacha with figuring out your status! May Hashem lead you on the right path. In the meantime, keep davening, fasting on Yom Kippur, etc. As far as you know so far, your mom’s gerus was valid. I wouldn’t worry about your prayers falling on “deaf ears” — I’m sure Hashem appreciates your efforts to get close to Him and do His will. If you have any doubts that Hashem desires the prayers of non-Jews as well as Jews, read through (or better yet, recite) the book of Tehillim (Psalms). King David is always calling on all people (even animals, trees, etc.) to praise Hashem.