One of the roles of the immigrations officials is to determine if you are wanting to enter the country for legitimate reasons, and for reasons that are within the rules of whatever class of visitor you are seeking to enter the country as (eg, a tourist, for business, for work, etc). They are also trying to determine if you are likely to leave within the time allowed for your visa type, and that you are not involved in any way in some form of crime - including smuggling drugs or human trafficking.
With very few exceptions, they can basically ask you any questions they want to in order to determine if that is the case. From my experience of having passed through US immigrations over 30 times over the past few years, they generally have a few basic questions that they will always ask ("what are you here to do", "how long do you plan to stay" type of thing), and then depending on the answers you give to those questions they will either accept your answer and let you in, or dig deeper into the details.
The fact that you might not be able to answer one or two questions completely isn't likely to be in itself a problem, as long as they are convinced that you're entering for legitimate reasons. Not knowing the profession of your host would be expected if you were to say that you were doing a House Swap/found them on AirBNB/etc, however not being able to answer the same question would be very suspicious if you claimed they had been a friend for 20 years.
Other questions I've been asked over the years include everything from details on what attractions I was planning on seeing (when entering as a tourist), details on what I was going to learn (when entering for a training course/conference), details about the position I was applying for and where it was to be based (when entering for a job interview), and details about who I work for and what I do there (when entering on a work visa). I've also been asked if I have any relations in the US, details of where I'm staying whilst I'm here, flight details for leaving the US, and even where I had come from, and what I was doing there.
Even if you do have issues with the initial immigration officer you will not be immediately rejected for entry, but instead will be taken to a "secondary screening" area where they will re-ask many of the same question, and potentially do further research to determine if you are legitimate or not. eg, they might call you host and confirm that you are staying there and that the reason you don't know their profession is because you found them via AirBNB.