If I set it as secondary, does it mean it's a fallback if my primary fails? If yes, it would wait for the timeout on primary before hitting the secondary. Result, slow connection. Or is not that how it works?
Generally, yes. Although if it's even half smart it should keep using the secondary, and periodically check whether the primary is back up.
I cannot figure out how my network comes into the picture for IPv4/IPv6. Isn't it the IP of the target site which is IPv4/IPv6?
No, the entire route must be IPv6. If your home network, or your network provider, or the target site, does not use IPv6, then you need to use IPv4. Neither my home DSL provider, nor my mobile provider, nor the hosting company of my web site, currently support IPv6, so for me personally IPv6 is largely a non-starter so far.
Also isnt IPv6 a superset of IPv4?
Not really. Quite some contortions are necessary to use IPv4 in conjunction with IPv6, for example: see
6over4 and
4in6.
However my Mac network settings have an entry for 10.0.0.1 which I do not remember ever configuring. If I am understanding this correct, I should change the values only for the router and leave the Mac settings alone. Is that correct?
Depends on what 10.0.0.1 is - if it's the router used to connect to the network it may do some useful caching on its own, in addition to being the ultimate reference for other devices on the local network. On my Mac it's set to 10.0.1.1 - the WLAN router.