How can I determine how much space it really has?
On Windows, use the tool h2testw. It's hosted on a german website called heise.de and you can find the direct download link here: h2testw.zip. It's easy to use. Open it up, select the drive, and hit start. You can find more information about it on this site. It will also perform a read/write speedtest.
On Mac or Linux, you can use the great alternative: F3.
You can most likely get it from your repo (sudo pacman -S f3 on arch, sudo apt-get install f3 on debian/ubuntu) directly.
It's usage is pretty simple. You have to mount the partition of the USB drive somewhere, let's say /media/usbd. Then cd /media/usbd into the directory and run f3write ./ until it finishes. This will write as much data as it can (should be 64GB in case of a fake 64GB USB drive that in reality is 8GB).
Afterwards, run f3read ./ in the same directory, it will now attempt to read back the data but fail after 8GB in our example. At the end, you will get a summary. This will also include read/write speeds.
Another way to do it using f3 is by using the f3probe command. From it's --help text:
Usage: f3probe [OPTION...] <DISK_DEV>
F3 Probe -- probe a block device for counterfeit flash memory. If counterfeit,
f3probe identifies the fake type and real memory size
In order to find out your disk device, you can run lsblk, then run f3probe /dev/sdX, replacing X with your drive's letter found out by lsblk.
Can I format it properly if I can get the above answer?
I wouldn't bother with that because...
Should I just return it and not try to salvage it?
...you can clearly expect this USB drive to be very faulty much sooner than a decent drive. Just ask yourself: If these manufactures would use high quality components, would they sell it at a fake capacity instead of selling genuine, high quality USB drives?
I've had several of these drives because it's basically free 8GB drives, so I thought when I was young (you get fully refunded if you buy on a reputable site). I've been setting up a partitiontable that would make me able to use just the ~7.4GB that were real, and then format those as FAT-32 and use them. They all broke within months of using. They'd end up not being detected by any OS at all.
Conclusion: If you ever find a too good to be true deal for a USB drive above 8GB capacity, always check it first. If it's fake capacity: Don't even bother. Get your money back and return it or throw it away. Unless it's a cute novelty USB drive, then do like me and keep it as a cute keychain or desk decoration.