1.How do I apply for a PAN card? How many days will it take to get a PAN card after applying and what is the cost?
Ans- It takes about 15 days to get a new PAN allotted.
However, PAN can be obtained in around 5 days if application is made through Internet and processing fee paid through credit card. Visit: http://pancardonline.in/pan-card-online-apply/

2. Where do you apply for a new one when you lose your PAN card?
Ans- If you lost original PAN card then you have to apply for duplicate one.
Duplicate PAN card requires same procedure to be underwent as that of original PAN Card. But there is change in the form that is required to be submitted for duplicate PAN card. http://pancardonline.in/how-to-apply-for-duplicate-pan-card/

3. How can one know how many accounts he has with his PAN number?
Ans- There is no such way to know number of accounts associated with PAN number.

A person may open bank account without providing PAN copy. There is only one way to find out i.e. by visiting every bank and asking them to check with your PAN details if you held any account with them. However, RBI and Income Tax can check number of accounts associated with your PAN detail.

4. If I know ones name and address can I get his pan number?
Ans- You need to know the persons full name and date of birth. You can find out the PAN Number in the given below link.  https://incometaxindiaefiling.gov.in/e-Filing/Services/KnowYourPanLink.html