Which apps cannot be disabled (without root)? I need to know more about disabling built-in apps. Some apps can be disabled, but there are some which has "disable" button disabled. 
Is there any way how to find out which apps cannot be disabled? (I know that disabling some of them (e.g. settings) doesn't make sense, but some apps look OK for disabling and it is not possible for them too). Is there some other problem with disabling them? (I heard that some of them enable themselves with restart of phone).

Thanks a lot for answering.
I think you cannot disable "system apps". A layman definition of system apps can be ones those are installed when you install the ROM.

there can be a few in custom ROMs and UIs that companies provide because they think it is useful.

if you have something like ESExplorer, I think you can see which apps are system apps and which are user apps.