How does emulated storage actually work? I recently bought a Xiaomi Note 4G. An amazing piece of technology. I transferred the apps I had on my previous device to it.

The reason I bought it was partially to have a good gaming experience. But what I witnessed is after you have filled your internal memry with apps and games you cannot free up space: there is no option to move apps to SD, a big disappointment. Even third party apps with root permission don't seem to work, but they hinted that my device uses emulated storage and that it treats both the storage spaces as one.

My question is, then: why can't I install apps anymore if I have 23 GBs of free space? Is there any workaround to this problem I am not able to see? I will be grateful if someone could help out here. Thanks!
This does not depend on stock Android, it depends on Xiaomi. Your system is only installed in a partition (system), it does not alterate the whole partition table on your device.

I had the same problem with my MI2S. Only recently I repartitioned the whole phone, giving 10 gigs to the apps' section. It seems like it's the only way. Here are the detailed instructions.

http://xiaomi.eu/community/threads/mi2s-extending-size-of-storage-partition.21391/

Obviously you have to do the opposite, as stillka is removing space from the data partition to give it to the storage one. Giving that you basically have to delete both partitions and recreate them with different size, the procedure is the same, you just have to make your own calculations as you have to give startpoint and endpoint, not size.

I did this procedure twice in a row, because the first time I also removed system1 partition to get another 500 MBs, and I didn't brick my phone nor the first neither the second time so, even if the procedure looks scary it is quite safe. Obviously it means losing every single data you have in your phone, both apps and such and personal data. So, you must use some backup app to save your apps and data and then copy the whole sdcard (including the backup you just did) to your PC, restoring once you recreate the partitions.

Note about chache and system1: you can also delete these partitions (really, shrink them to 3 MB - the minimum to make them ext4 filesystem - as you shouldn't change the original partition table) to gain even more space, but there are consequences.

Cache: some people say this partition is used by Google's Play Store to temporarily store (pardon the play on words) apks files before installing the app to your phone. That means, if you remove it you won't be able to install apps from there anymore, and if you shrink it too much you will be able to instal small apps only. If you use other sources than the Play Store (or, maybe, even Xiaomi's official market) you should be good.

System1: this is for the fake dual boot MIUI uses: every time you update your system through the built-in Updater app, the new ROM is written to the system you were not in, alternating between the two at every update. This is to have a correctly functioning system in your phone, not overwriting the previous system while updating (so, it is like a system backup). If you remove it, you won't be able to use the Updater app anymore, you should every time flash the newer ROM when you want to update. I did not do this as I use MI2S' Sepcial Edition MIUI 6 ROM, and the only easy way to install it without third party tools is installing the regular v5 ROM and update with the Updater app. Your choice.