Is a person having ITIN eligible to have a bank account in his name. If yes, what type of bank account? Can he also get a credit card?

ITINs are strictly for tax processing, not for identification. I'm sure that your passport or visa is enough to get a checking or savings account. If you need a credit card you may want to look into something like a pre-paid Visa or Master Card. They work like a credit card, but without a monthly bill. Some do have a nominal monthly fee of $3-$5, but you are only charged if you have a balance on the card. (It's similar to a finance charge on a credit card.)

Many banks and credit card companies take ITINs in lieu of the SSN.

That is not the intent of the ITIN, but the banks and credit card companies in question do not care.