Can we have unprotected sex without condoms? For example can I take just pills? If I can take then which pills are good and when I should take?

You can have unprotected sex anytime you want.. Just expect the likelihood of getting pregnant to be far, FAR higher than if you used protection.

Pills? Normal birth control pills need to be taken for a full month before they are effective.

If you are having sex, you should be using condoms and on birth control pills.
The pills have to be taken corrected and none forgotten.

There is no "safe" time to have sex, even using condoms alone, they have up to a 10 percent failure rate.

No protection greatly increases the chance of having a baby