It looks to me that the Oleg's firmware for more or less all Asuses is of the same size, and that Premium has twice as much flash capacity? Does it mean that it would be possible to add a lot of programs to the flash on the device?
yes Premium has 4Mb+64kb available for user
Do I have to build my whole firmware package for that?
no
What does "flashfs save" do? Does it save only some conf or is it a simple way to add the whole programs to the flash?
in combination with flashfs commit it saves content of /usr/local and the files mentioned in /usr/local/.files in the internal router's flash
How can I know how much space on the device I have remaining?
When you execute flashfs save the tar.gz file is created and it's size is shown to you. This is how much space it will occupy in flash
2) my answer is possibly yes, try
However, remember, that if you put let say 4Mb in flashfs, then after startup they will be taken out of it, extracted from tar.gz and placed in ramfs. And it will occupy considerably more space in ram than 4Mb. So the more you save in flashfs, the less free ram you have. In conjunction with your desire to use it without flash the real probability of success gets lower.