Non working SoftwareSerial and delayMicroseconds() on ATtiny85

I am currently using the ATtinyCore from GitHub - SpenceKonde/ATTinyCore: Arduino core for ATtiny 1634, 828, x313, x4, x41, x5, x61, x7 and x8. (That is what you meant by Hardware profile, right?) I initially used the ATtiny core provided by MIT, but I stopped using it when I realized it was 5 years old, whereas the ATtinyCore was updated 2 days ago. I am uncertain if tuning my internal oscillator would do anything, so that is the next item I am going to try to address.

As soon as I can figure out where to get an oscilloscope, I will do so.

Thank you for your advice, Perehama and DrAzzy.