Hello!

My old thermometer only measured to .1 as well, and that was perfectly fine for temping. I'm currently using one that measures to .01 and although I'm finding the extra detail interesting it's not made a huge difference really. You should be fine with the one you are using
Some ladies do have flat temps, although it can also be a sign that the batteries on your thermometer are starting to run out. Is it a new thermometer?

about having a few days of flat temps - I've had charts where my temp barely changes for a few days too