The term "operating system" doesn't have any universally accepted definition. If you want a better answer than what's already been posted, you need to define your terms. The terms I am referring to are: OS, simplest, possible, program, (note the commas between those terms) maintenance, exist, system, ready, prompted and interact. And I mean in a technically acceptable and adequately specific manner. You can certainly look at DNA as "a program". Same thing with holes punched into a piece of paper (or words written in a book). So, given these (and a practically infinite number of other) examples. Can dna exist without "an operating system"? Obviously the answer is yes. So, can a book exist without anyone who can read it? Can dna exist without a cell to implement its instructions?
I've always said that once you know the terminology of any discipline, you're 90% of the way to having a preliminary knowledge of it. In the days of the first chips, and electic circuits with memory, there was no (soft, nor firm) operating system. The voltages went in through the op-amps and you got output of some sort (a switch was toggled, a light lit, etc.). It isn't unusual for questions to be asked without context which require context to be answered. In a modern computer, the OS is a (group of) program(s). As long as some method exists to input instructions (code) into a device (system) capable of changing state, you have the ability to input "a program". But that is typically useless without one or (usually) more methods to receive output (determine what the 'final' state configuration is).
Programs don't "interact" unless they are instructed to (or unless they interact with the OS (or hardware) which in turn may interact with other programs). A typical (modern) computer "system" consists of one or more cpu's, volatile working memory, various other chips (graphics, audio, ports, interrupts, etc.) and one or more storage devices as well as connections to the internet. I don't really understand your question 2. Are you suggesting that there is some magic genie capable of randomly recognizing a string of zeros and ones as "a program" and then loading it so that the cpu (etc.) can run it? Some programs reside in working memory, but generally working memory is volatile (meaning power to it needs to be maintained), fast but volatile. These programs may be loaded into working memory from hardware or much more commonly from storage (one of the functions of the OS is to bootstrap itself (using hardware) and then load all of the other junk (often in a cascading fashion). Nothing is "instantaneous", logic switching requires clock cycles and voltage changes. So what you mean by "residing" in the system isn't clear to me. If you compare the speed of cpu register operations to the speed of accessing working memory and then to the much much much much much slower access of storage, then you will realize that one function of any modern OS is to manage the flow of information thru the system so that you don't perceive the delays and laggy behavior which would be quite annoying in a linear "wait until you need it, then load it" system. Obviously a modern OS is so complex that no one person can (imho) understand it all.