can we the store the users in our own membership table other than aspnet_membership table.
You can. Take a look at custom membership providers:
Also, search CodePlex for "Membership Provider" for some pre-built ones.
Once you have your custom membership provider, it's just a matter of changing the web.config to point to it instead of the SqlMembershipProvider.
Let’s say, I need to authenticate user with login name, password and secure code, means implement some code within custom membership provider right. Can we modify code within custom membership provider ?
Yeah, that's the whole point of a custom membership provider. You can modify one that's been posted on CodePlex, or write one from scratch.