Well, I wouldn't call it a library - it's built into the core. What's more important is that it's a software implementation. So, like SoftwareSerial, you can't receive characters while sending or vise-versa (and get/send gibberish if you try), unlike Serial on a board with hardware serial ports. This is an important difference between hardware and software serial. Software serial also often gets flaky at higher baud rates.
Pretty sure the Serial portion should work identically. Use SoftwareSerial only if you need to put it on different pins (the motivation for the builtin serial is to put the serial on pins such that it can use the analog comparator's interrupt so it leaves the more useful INT and PCINT interrupts available)
I have not had a chance to test external reference - I couldn't find my tiny84 testing board last night. Honestly, I've got so much on my plate this week I may not be able to test it myself until next week. If it doesn't work, that's a bug in my core that I would consider a priority for the next version.
You need to do "burn bootloader" once (with any core) on a virgin chip to set the fuses, even if not using a bootloader, even on a board for which no bootloader is supplied. (that's the only time the fuses get set - they don't get set when uploading the sketch). The boards you bought probably had this done by the manufacturer, but when you start getting bare chips, you'll need to do this.