Indira, the length of time it takes to convert will vary depending on which sect you choose. And yes, it can take some doing to convince a rabbi you want to convert. My understanding of this has always been that due to the history of persecution, they want to make sure someone's desire is sincere before proceeding. At the very least it would take a year as almost all rabbis will want you to go through the cycle of the Jewish year.
Depending on the sect, I'm not sure belief is always important. It might cause people to wonder why you're converting, but after all, Israel does mean "he who struggles with God". Struggle, and dissecting the text, and questioning, is a strong part of the tradition (leaving the ultra-Orthodox out of it).
I love Jewish ethics. That practice comes first and hopefully your heart will follow. So you do that good deed, not always because you want to and certainly not to get into heaven, but because it's the right thing to do.
I like that there is no concept of Satan in Judaism. And that they do not believe that sex is bad (unless coercive). In fact, a man refusing his wife sex is grounds for divorce in the Talmud.
I like that there is so much to learn you can never master the whole thing.
So do your research as to which strain fits your ethics and then see what is available in your area. Many schools in my area have an Introduction to Judaism type class. For those who are getting married, for Christians, for people who are just curious, and for those who want to convert.
It sounds like you may have a Jewish ruach, so don't ignore that voice, just see where it takes you!