You are eligible to apply for Medicare during your initial enrollment period which is a 7 month window. 3 months before turning 65, the month you turn 65 and 3 months after turning 65. 

If you are already receiving Social Security benefits you will be automatically enrolled into Original Medicare, otherwise you will be eligible to enroll during your initial enrollment period that starts 3 months before your 65th birthday.

If you miss your Initial Enrollment Period you can sign up during the General Enrollment period that occurs every year January 1st through March 31st. Coverage becomes effective the month following your enrollment date.

Yes, there are penalties for not signing up for Part B of Medicare and will be added to your premium.

If you need a new Medicare card you can order a replacement card by phone at 1-800-772-1213, or online at the Social Security Administration web site. Make sure you have your Medicare number ready when you call.