What if I, hypothetically, used my mobile data on my phone and created a new account, and on my other phone, using Wi-fi, logged into this account.
Yes, each phone would have a different public IP address because they are connected to different networks.
Are mobile data's IP's always the same for the device/plan, or do they change/rotate based on you location? Do we know? if we don't, would I be allowed to test this?
The short answer is that it is very difficult to do a "set and forget" IP ban on somebody who connects using a cellular network. The precise answers to these questions depend on the technologies and protocols used by the network; but in general, any IP address used by your device through a cellular network is very disposable.
Several devices connected to the same cellular network (which, predictably, would have the same carrier) may have the same public IP address, but those IP addresses generally roll over very often. Also, as you mentioned, your IP address is likely to change if you go to a different place – it might persist between cells in the same network, but definitely not if your phone connects to a completely different network. (The range of these networks depends again on the infrastructure.)
It is possible to combat this by blocking ranges of IP addresses (as ISPs are generally given particular ranges of addresses to use); but especially when you're talking about public-access networks like these, you run the risk of blocking people who have nothing to do with the person you're trying to keep out.
Home networks are easier to work with because they're generally less "dynamic" (i.e. the address is less likely to roll over arbitrarily), and the same people are likely to connect to their home network.
I'm wondering if dupe accounts could go undetected via mobile data, and if constantly changing IP's have to do with mobile data.
If you were careful with how you did it (and perhaps knew a bit about how Q2A reports IP addresses to us), then yes, you could prevent two accounts from ever having overlapping IP addresses. However, IP addresses are far from the only tools we have to track funny business – common sense and experience makes it easy to notice, and IP addresses can confirm our suspicions.
Cellular networks absolutely have to do with constantly changing IP addresses, but it's still possible to use IP addresses to "confirm suspicions" as outlined above if addresses used by the same people are similar (i.e. some of the numbers are common). It's a bother insofar as bans won't persist between accounts, but it's generally not hard to see which accounts belong to the same person.
I'll also clarify some of the things HT mentioned.
IPs from mobile data are different from IPs from normal internet connection. Mobile will use IPv6, and normal internet connection will use IPv4, if I remember correctly, and they are visibly different, so it's easy to tell if somebody is using data or not.
IPv4 and IPv6 are different labelling systems used to assign IP addresses. IPv4 was the first one created and it's still used very often today. However, IPv4 only reserves 32 bits of memory to store each address, which means the total number of possible IPv4 addresses is limited to exactly 2^32 or 4,294,967,296. This is not nearly enough addresses to service the billions of internet connections in the world, which is one reason why IPv6 was developed.
IPv6 addresses use 128 bits and therefore have 2^128 possible addresses, which is very convenient for cellular networks which change their addresses very often. However, there is no reason why a home network couldn't use an IPv6 address – it's not a true distinction. IPv4 and IPv6 do look different, though; IPv6 addresses are obviously much longer and use hexadecimal numbers instead of normal base-10 numbers to make them easier to read.
Any IP changing shouldn't be of any concern, as IPv4 addresses can also change, however, I think that it should be of less concern if IPv6 addresses change often, assuming they change with location.
Any network can change its public IP address, so it's always something we should keep in mind when managing IP addresses. But, as described previously, it's not as problematic as you might think.