I have created a business Gmail account from Google Apps with custom domain. I want to transfer my emails and contacts from my old Gmail to this one. The thing is, in Gmail settings there is a tab called "Accounts and import," while in my new business account there is "Accounts" there is import functionality I guess. Is there another way to do this?
You can always export your Contacts to a Google CSV file and import that file to your new Contacts. Just hit
Gmail in the upper left corner and select Contacts and find the Export option.
I see that the normal Gmail Import functionality is not available for Apps. You can always add your old Gmail as a POP address and import the mail that way. Here you can enable POP in your old inbox. And here you find the configuration you have to enter in your Apps account.