Increasing the alphabet for passwords doesn't really make your password stronger than if you would just increase it's length by a character or two, or better yet three or four. But, given that I can't imagine too many password crackers checking for more than a couple common extended characters, it's probably not that bad. Still doesn't excuse passwords like pɹoʍssɐd though.
Every password manager I've used (granted only a few) will generate random ones for you. Is this significantly more secure than a random 18 character string?
These characters aren't easily type-able and most password crackers that I've seen use common ascii/ansi characters not obscure characters like this... It's all relative I guess. There obviously exists a case where these characters aren't helpful.
Can you realistically crack an 18 character random string, even if you know the character set? I mean, I realize that technically increasing the character set would make it harder, but for any web-based service cracking something with 62^18 (or more if other characters are used) possible combinations is impossible in the real world.