Is there a way I can create tasks that have no time estimate?
Yes, it just depends on your Jira configuration. However, as you stated, once you have logged time on it, Jira deducts you're a time tracker... and thus, assume you are interested to know by when you no longer need to log time on it (i.e. you want to know your remaining).
Either you should not be logging time at all at these tasks or they should have an initial, ballpark estimation that will be decreasing every time you log time on it.
need to adjust the remaining to 0 each time I log time on a meeting or
Is there any specific purpose on logging time on a task and still keeping the remaining fixed on zero if you know that tomorrow you're likely to be logging time on it again? In our project, we have such tasks just to have transparency on how much time such meetings absorbs from the team. They're never added into the iteration, but we can forecast our work more accurately and (have evidences to) say to any user that's not realistic to expect anyone to work 8h / day (sometimes, appeal to the common sense doesn't work).
Having that said, the answer for your question should be 'stop fighting something that's trying to help you' (or else, make it clear in your question why it must be always zero).