How long did it take for you to become flexible doing yoga?

There is no one fixed answer. It depends on the individual who is practicing Yog. If the person is young, generally the body is more flexible.

Generally, it takes about 2 to 3 months of regular daily practice for your body to become flexible. It took me a good time to start doing Padmasana.

As someone has written here, respect your body while doing yoga and dont compel it to to postures that it can not naturally. You will end up having internal injuries.
Depends on you greatly. I practice yoga every day and wear special yoga pants to feel all my muscles stretching enough. You can start from twice a week training and simply check how your body reacts. I can assure you that once starting practicing yoga, you won`t give up.