Help With Religious Life

This is a bit of a long intro, so I apologize in advance, but I would appreciate any feedback or advice if this kind of post is allowed.

My mother’s side of the family is Ashkenazi Jewish. My grandmother had been born in Germany to a Russia-native family that had been imprisoned and survived the holocaust. After immigrating to America they became Christian. My grandmother married a non-Jewish, Christian man and raised my mother Christian, however, had taken her to a messianic congregation for sometime (yikes, I know, but it gets worse). I was also raised Christian but in a fundamentalist environment. When I was around 9 my mother and grandmother became heavily involved with the local messianic community and began taking me to a messianic congregation, which I attended until I was about 14. I grew up celebrating both Christian and Jewish holidays (although the Jewish holidays could easily be described as being “watered-down”) and I had some exposure to Hebrew and (stolen/misused) Jewish prayers. Our “Rabbi” had gone to rabbinical school and was originally orthodox I believe, but he converted at some point in his life and mostly preached about Jesus (I think this was just his way of holding on to his Jewish identity but obviously going about it in a very wrong way). In fact I’m pretty sure that my family was the only ethnically Jewish members there aside from the Rabbi.

As I became a young teen and became more interested in my Jewish heritage and did more research for myself, I slowly became more and more uncomfortable with being a part of the messianic movement (the congregation itself was also a bit of a toxic/borderline cultish environment). I eventually stopped going to services altogether.

About a year or two ago I bought myself an actual Hebrew to English Torah (I also already owned several other legitimate Jewish prayer books and literature). Recently I came upon a local conservative synagogue and I attended a service and bar mitzvah as a guest. I really liked the environment and the Cantor (they do not have a rabbi) seemed very nice.

I am currently in the process of setting up a meeting with the Cantor to discuss becoming a member in the future, and I plan on regularly attending as a guest until then. I already have several yarmulkes to wear to services and I am trying to get into the habit of reading Torah every day.

I just have several questions about this process.

Since I am ethnically Jewish but raised Christian (I am about 1/4th, so I’m unsure if that is considered “Jewish enough”) will I have go through the conversion process or will I just have to study extra hard?

I was told to wear nice clothes to services, last service I wore dress pants, a sweater, and a peacoat (as well as my yarmulke). Is this acceptable? As the weather gets hotter will short sleeve polo be acceptable? Or is long sleeve better?

I am really hoping to eventually learn Hebrew. I believe the congregation offers adult classes. I am also a passionate learner and already study languages in my free time. For anyone who learned Hebrew as an adult, how long did it take to become decently proficient, or at least proficient in services done in Hebrew?

I would also appreciate any suggestions for Jewish literature to help me study and get exposure to true Jewish life.

Thank you very much for taking the time to read this.