Hi @Elli0 and @Clare0
I have to preface this with "do not construe this as legal advice" because I am not myself an attorney, and even if I were an attorney, I could not offer legal advice on a help forum. Furthermore, it's important for all to understand that any advice offered on online Q&A forums, even if offered by a licensed attorney, cannot be construed as legal advice. See here: What is Legal Advice
I have spoken to an attorney about exactly the question you presented, namely, as regards the definition of "subletting" or "subleasing". I asked that question very specifically, precisely because I was aware that many tenants are under the mistaken belief that they are not subletting, if they are present in the apartment at the time they are renting out a bedrooom to a guest. (See this post I posted a couple months ago: A Delicate Question )
I was working at the time as the property manager for a landlord who had such a problem with one of her tenants -- she discovered that one of her tenants was doing Airbnb hosting, having short term guests, in violation of her rental agreement in which she clearly states, "no subletting". The language in her lease said "no subletting" but did not say "no Airbnb hosting or short term renting to guests" and I wanted to find out if she needed to clarify the language in her lease. So I, as her property manager, spoke to her lawyer, and I was told, by this attorney, experienced in tenant-landlord and real estate law, that subleasing is ANY form of renting out property by a tenant who is renting that property from the landlord. This attorney told me that it was not necessary to say, "no Airbnb hosting" or "no short term renting to guests" , because the "no subletting" clause covered those things and prohibited them. (By the way, this tenant of hers who was violating her rental agreement and doing Airbnb hosting was given a 3 Day Notice to Cure or Quit, which means, that if he did not stop hosting within 3 days, he would be evicted. He stopped hosting immediately.)
It is completely beside the point that you are present on the premises when you are renting out the bedroom to guests. That doesn't make any difference. If you are taking in money from someone using any part of your apartment for accomodations, you are subleasing or subletting, and thus you are in violation of a lease which prohibits subleasing. You would not be in violation if your guests were not paying you anything -- for instance if they were relatives , or if you offered a place for folks to stay for free as with Couchsurfing. But any time you are taking in money by offering accomodations, you are subleasing, and whether or not you are also there is irrelevant.
So in answer to your questions ---
(1) Yes, the legality of Jersey City law is totally dependent upon you having permission from your landlord. Simply put, any landlord's rental agreement trumps city law, when it comes to the subject of short term rentals. If a landlord prohibits short term rentals, the city's regulations on the issue are moot. Your rental agreement and not city law is the final word on this issue.
(2) As stated above, yes, short term rentals are still considered subleases/sublets even if the tenant resides on the premises at the same time that the guests are present. You are still renting the space out, so you are sub-renting or sub-leasing.
(3) I don't know the answer to your question about Jersey City law on roommates. I do have a feeling, though, that you will not be able to make the case that sequential short term guests constitute a "roommate." I would think that even if you could, as in NYC, have a roommate without landlords' permission, it would have to be an actual permanent roomate. Perhaps a tenant agency or rent board in your city would help you with that answer.
(4) No, offering a shared space doesn't mean you have a roommate situation instead of a sublease. Consider, that if that were the case, then any landlord's no subleasing clause would then be totally ineffectual, as no landlord would be able to prohibit subleasing, if every tenant could argue that the subleaser was really a "roomate" and that the tenant was allowed to have roommates.
I empathize with you in trying to think hard about this situation and explore all possibilities and permutations so that you can do what you would like to do, but particularly if you are already on the property managers' sh** list because you have had complaints from ghetto neighbors, and been ratted out, it will be challenging for you going forward, to try to do short term rentals.
Most landlords will NOT allow tenants to do subletting or short term rentals, so it would be a mistake for any tenant to rent any apartment with the idea that they can do Airbnb hosting there, unless they have permission from the landlord to do that at the time they rent it. In general, the business of renting out property, is a business for those who own property. Airbnb can mislead many tenants into thinking that surely they can be Airbnb hosts, because it's so easy to create an account and click on a few buttons and become a host. Yet you can no more be an Airbnb host renting out a room in your apartment without your landlord's permission, than you can rent out the car you borrowed from your neighbor, without that neighbor's permission. So I suggest folks don't start renting out other people's property without first asking for permission -- it's only respectful.
That said, there are many exceptions out there, and there are some very fortunate tenants whose landlords do happily permit them to do Airbnb hosting. So if that is what you want to do, it is good to intentionally seek out those rentals which permit it. THis is not likely to be easy to find, particularly as there are vastly more tenants who want to do Airbnb hosting than landlords willing to allow that.
I suggest talking to your property manager and/or landlord, and or the local rent board or tenant agency, to find out answers to your question about roommates, and what type of roommate arrangment would be permissible for you to do. Then try to find a solution within those parameters.