Well first, I wouldn't pose your preferences as questions.
I would say what salary I am aiming for if their range is too low for me to seriously consider the offer, otherwise, there's no point in wasting either side's time.
As for remote, I also wouldn't ask about that, I would just specify that remote is a priority for me.
If it's a matter where I could be sweet talked into taking their too low salary as long as I had sweeteners like excellent benefits, remote work, or whatever else, then again, I wouldn't ask, I would just indicate that those sweeteners could compensate for a lower salary.
I feel like you first need to really hammer out what it is that you want to achieve with these.negotiations and then just try to be direct about what it is that you want.
Negotiating isn't as much about being strategic and saying specific things as it is about finding a way to operate from a position of confidence.
Again, how would a supremely qualified, rock star candidate express their desire to work remote?
Would they ask if the environment was "remote friendly?"
No, they would come out and say "the ability to work remotely is a major priority to me, so I would strongly factor that into my decision between competing offers"
But you need to assess how important remote work is to you, compared to benefits, vacation time, salary, etc. You need to know which things to push for so that you communicate clearly what you really want.
If you just suggest that you are interested in remote work, and that their stated salary is lower than your minimum, you haven't made it at all clear how important remote work is, and if it will impact your salary demand.
So figure out what you want and then tell them how to win you over and then see if they are willing to give it to you. Just flat out, directly communicate what it would take to get you to work for them. Don't make them guess based on questions you ask, give them the exact recipe.