I converted from Evangelical Christianity to Islam 2-1/2 years ago...but before I took that step, I spent years studying not just the faith I left and the faith that I embraced, but other faiths as well. I'd say I studied Islam in earnest for at least 10 years before taking the step to convert.
Now that I'm a Muslim, I continue to learn--though before it was mostly academic, it's now "how must I live my life in response to this?" I don't think anyone ever fully learns the depths of any religious tradition in a lifetime...nor do I think I'm so wise as to ignore all the learning and wisdom of the ages that came before me--I'm not that special. Sure, they might be wrong on many things, but getting a lot of different points of view and not just relying on your own is one of the major keys to wisdom.
I can't imagine changing religions--or staying in a religion, for that matter--unless one engages one's whole self into it--body, mind and spirit. I don't think a warm feeling in my heart or just the worldview I have that was formed by the culture or family in which I was raised is an adequate way to weigh religious truth. The mind needs to be engaged, and taking a momentous step to convert to another religion shouldn't be done based on an emotional response.
The "normal time" to know my religion well? I guess to learn the basics of the five pillars, you can learn that in a month or less. To understand the depth of it? More than a lifetime. Between those two extremes, I'd say it depends on how deeply they study and pray and follow the other pillars of Islam. I wouldn't trust a teacher who has studied less than 10 years or so, though.