IMHO your first two questions should be solvable to anyone calling him/herself a programmer, be it junior or senior, straight out of school or self-taught.
If I see that the interviewer is struggling with either of these, I would try to rephrase the problem, and check whether (s)he fully understood it. Then encourage her to use pen and paper, whiteboard, draw figures or whatever approach she prefers to tackle the problem. I also ask her to think aloud, to get a view into her thought process and if needed, give little hints if she is on the right track just doesn't dare to advance, or has some obstacle. But if even several hints don't help, or - as you mentioned above - I end up solving the problem for her, I would probably finish the interview to stop more wasting of our time. In an interview, I am always striving to see and focus on what the candidate knows, instead of what she doesn't, but if I can't seem to find any significant knowledge, I give up after a while.
The 3rd and 4th ones are somewhat more difficult, so I could accept if a junior couldn't get them, if (s)he otherwise demonstrated a good problem solving approach and enthusiasm. But for a senior, they are still a must.