So, I went through the whole password reset process myself just now, and I think I can address all of your points without having to corral a dev.
One:
That green check doesn't check whether your credentials are valid. It's only there signify that the field has been completed in a way that is acceptable. The things it checks, as far as I'm aware are: A) The username field has at least one (1) character in it, and B) The password field has a minimum of 4 characters, which is the required length of passwords.
Two/three:
These two problems are tied together. Tested a few times on a Gmail account and mine had no issues displaying the full email. The second half was not recognized as a signature. This leads me to think it's part of your personal Gmail settings (mine were left at the defaults). Tested on various other email clients, including on mobile devices, and none of them ran into this problem.
The email does not ask you to change the password yourself. After clicking on that link, you should be taken to your profile page, automatically logged in temporarily via a "token" (which you will notice in the link provided in the email), and a yellow notification bar appears near the top of the page saying: "A new password has been generated and sent by email. You can now modify it in your account settings." At this stage, you, the user, were not required to change your password in any way yet.
Four:
Again, does not ask you to change your password. See above.
Five:
Wasn't part of the process. Email should have been sent without you having to create a new password. After all, that would be redundant since we are sending you a new, randomized password. There's no reason we would ask you to change your password before that.
All in all, I don't know why you ran into so many issues. The root cause seems to have been issues with display settings somewhere that led to subsequent misunderstandings. The password reset system could be better, because everything can always be better, but I don't see that anything needs fixing or tweaking right now.