I have an AC750Wi-Fi Range Extender RE210. Can I ha ve a different password for the range extender wifi from the one used to log into the original wifi network?

No it is impossible.

Can I achieve what I want using an Access Point like the TL-WA801ND?

Are you talking about this password?

Yes. I want to create a separate wifi network which accesses the Internet through an existing wifi network. The two should have different login details and computers on the existing network should not be able to access the new network. I think I can achieve this using an access point like the one mentioned before, possibly in Bridge mode?

Main router doesn't have "Guest Network" mode?

I don't own the router or have access to setup. Whilst I might be able to negotiate to set it up the way I want, it's not a nice solution. Much better to be in charge of things myself.