>I always underline ш and write a line over т (which looks like m) to distinguish them

Having studied Russian in college, I assumed that all Cyrillic script included a line over the т, because otherwise readability goes to hell. Is my impression here based on (a) an opinion of my Russian prof expressed as a universal rule or (b) a thing that's universal in Russian specifically, but not Belarusian Cyrillic or other similar contexts, or... something else?

I'm inferring from your post that you are a native user of Cyrillic who has also learned English. I'm the reverse (well, at least I took Russian in college; I was never fluent then and remember almost nothing now). Something interesting happened to my cohort of Russian learners back then, and I wonder if it's common for folks going the other way.

After we got comfortable with writing Russian in cursive, we found that Cyrillic letters worked their way into our English script. Often, we wouldn't even notice, even when reviewing our notes later. I discovered I'd done this when I loaned some political science notes to a friend, and he couldn't read them because I'd unconsciously mixed Cyrillic and English script. I could read them fine, and so could my Russian-class friends.

We mentioned this to our Russian prof, and he laughed and said it happened to people every year, but he could never figure out who would be prone to it. Sometimes it was top students; sometimes it was people who were struggling.

(It was in this era that I ended up pretty much abandoning cursive, because Cyrillic never crept into my printed handwriting. 35 years later, my cursive is abysmal.)

Did you end up mixing script in your native handwriting inadvertently?