Create several Gmail accounts anonymously using only one Android tablet without letting Google know that they are created from the same single tablet?
What you're talking about is not sufficient. As seen in answers to this question, some tablet devices do have IMEIs even though they don't have a SIM card slot or telephony capability. Besides, all Android devices come with some extra unique identifiers. Both the Bluetooth and Wi-Fi hardware include a MAC address, which is used in those network protocols to uniquely identify the device. These can be read by any app with the appropriate network permissions, including the pre-installed Google apps.

They can be overridden in software, but the true values are part of the hardware, so the OS can read the true values anyway. (And of course a factory reset would undo the override anyway.) The OS can also read the unique identifier that's a part of the CPU itself and can't be overridden. If you really don't trust Google to this extent, you need to install a custom ROM (which still leaves open the possibility of a malicious binary driver).


  I would like to make sure that Gmail accounts are free and that there is no need to provide Google with my credit card information, my billing address or my real name. Is this correct? 


Yes, that's correct. You'll be offered the opportunity to add your credit card details when you sign up, to enable buying apps on Google Play, but that's not mandatory. They'll also pester you to add a phone number or "backup" email address, to aid in recovering a lost account and for confirmation after an unusual login, but again, this isn't mandatory.