Is there an upper limit to how often users may ask a question? I am doing masters level research so my questions are not "homework dumps" or anything that I haven't already searched for extensively, banged my head against a wall thinking about, etc. I try to be sufficiently specific that I don't get more direction than I really need, but if I'm having a good week there may be a domino effect of fruitful interaction here, progress on my part and more bite-sized questions. I just want to use this resource appropriately.
The only technical limit is that you must wait 20 minutes between questions (this only applies to low-reputation users). A few of the biggest site in the Stack Exchange network have additional limits: a maximum of 6 questions per day and 50 per rolling month, but these limits do not apply here. (Source: The Complete Rate-Limiting Guide)
There isn't a number that I'd put forward as a limit, etiquette wise. If you find yourself asking 50 questions a month, you should probably rethink your participation — but even that is highly dependent on the quality of your questions.
The important thing is that you ask good questions. As long as you do, I expect that nobody will mind, or indeed care. If you're imposing on us, we'll let you know progressively, via comments asking you to improve your questions. Only a pattern of asking low-quality questions would be abusive, and then the problem would be the quality well before volume became a concern.
As a masters student, there are undergraduate-level questions that you should be able to answer. I encourage you to spend a bit of time answering as well: it's a great way to organize your thoughts about things you already know, and a mini-practice for when you'll be writing up your research or doing some teaching. But this is only a personal encouragement for your own sake, it's perfectly fine to participate here only by asking questions.