Files in internal storage are copied to the external ext4 volume on the SD. The internal volume is not formatted. It is left intact. You can see for yourself by powering down the phone, removing the SD, and powering on the phone without the SD. If you observe the amount of space in Settings->Storage right before and right after the file copying, you should see the amount of used space (apps, etc.) is the same but the amount of free space is increased, just as one would expect. I hope that makes sense.
A class-4 card is probably not fast enough. You're likely to experience lag. I'd suggest getting a genuine Samsung or SanDisk class-10. If you're in the US, you can get a Samsung EVO 16gb for about $10, 32gb for $13, 64gb for $23 at Best Buy, Amazon, Walmart, etc. There are faster cards like Samsung PRO or SanDisk Extreme, but they cost more.
As for using swap space, my understanding is that it won't speed things up for you. In server and some desktop setups, swap is used to give the illusion of having more ram. The virtual memory helps with context switching. In a mobile setup, swap is less relevant, but there's one case where swap is useful. Having swap helps apps that get evicted from memory keep their states and transient data. In some apps like web browsers, that means web pages don't need to be reloaded or refreshed when you switch back.
You can create a separate swap partition or use a swap file. This hack shouldn't interfere with using swap, unless you somehow require the 2nd partition of the SD to be the swap partition. There is probably a lot of info you can find online if you want to do it.