Congratulations on your conversion!
The answer to your first question is: Yes, you received a new soul and retain the “old soul” as well! There are many sources which confirm this and the meaning is as follows.
The deeper, Kabbalistic sources explain that every Jew experiences what is termed an “expansion of the soul”. For example, on Shabbos evert Jew receives a “nashama yeseira”, or “expanded soul” for the duration of the Shabbos day. This is in order to be a receptacle capable of receiving all the spiritual energy showered upon us on Shabbos. This does not mean our “weekday soul” is replaced by another soul, rather our weekday soul is expanded . Shabbos, which contains a bit of the next world, allows for that “expansion” as the soul enters into the next-worldly space of Shabbos.
The entire Jewish nation received permanently expanded souls at Sinai, where the Israelites all converted to Judaism. The Abrahamic souls of the original Israelites were expanded to become suitable receptacles fit to receive the immense spiritual energy within the Torah.
Every gentile who converts to Judaism experiences his or her own, private Sinai experience at the moment of conversion.
The souls of those who decide to convert are considered unique even before the conversion. They contain a spark of a Jewish soul, serving as the impetus to take this monumental step.
Some explain that the souls of converts belonged to individuals of the different nations to whom God offered to receive the Torah, even before it was offered to the Jews. When the nations turned it down, there were individuals who indeed desired to accept it but couldn’t, as they weren’t offered to break off from their nation and receive the Torah individually. The souls of those who truly wanted to accept the Torah at that time have been waiting, anticipating the time they could make good on their desire to join the Jewish people and the Torah. That spark would not let them rest until it was fanned into a full flame, and they convert to Judaism.
The original soul which brought this all about is still there and intact, now fully expanded into a “Sinai soul”. At the moment of conversion – his or her private moment of Sinai – the convert becomes a vessel fit to receive and retain all the holiness of the Torah for the rest of their lives.
Although the original soul is present, the newness is sufficient for the Talmud to consider the convert as “katan shenolad”, like a newly born person. This has many ramifications in halacha, Jewish law. For this reason, some authorities rule that a convert should recite the blessing you mentioned, because you have been “re-created” as a Jew. Although some disagree, I side with the authorities that you should recite that blessing. This is in order not to be different than the rest of the Jewish people, as you are now fully Jewish in every way.
Best of success in your continued learning and growth. And welcome to the family!
Rabbi Yerachmiel Fried