1You are able to use both them together but I advise you — it will be a mess. And you gotta hope that you won't have any kind of conflicts between class naming and other general styling. My recommendation would be to use one and only one.
1Sure. It actually makes for an excellent developer experience since Material UI is a great component library but is missing utility classes, while Tailwind is a great library of excellent utitility classes. Utility classes make tons of sense for modern component based front ends that consume JSON data. XML style markup, it turns out, is actually great for visual stuff, not so great for data -- for which it is needlessly complex. Small but important tip: make sure you add important: true to your tailwind.config.js file, tailwind will be of limited use otherwise.