The matchmaker will come, even if you have only one Connection / Connexion, and have never connected to another. She will show up a couple of days after your Tamagotchi character becomes an adult.
About your other questions...
Quoting the TamaTown FAQ from here (
https://www.tamatown.com/faq.html ):
Q: How do I visit my parents or grandparents?
If your Tamagotchi is currently in the 2nd Generation or higher, you can view and meet your "parents"—the previous characters in your toy—online. After obtaining a password from your V3 toy, go the "Parents" home at Tamatown.com and enter it there for up to three different visits.
Q: I can't access the "History" menu on my V3 toy! Why?
The "History" menu, located in the "Family" section of your Version 3 toy is a new feature that allows you to view the previous Tamagotchis that unfortunately didn't survive under your previous care. This memorial will help you to remember those characters that have returned to Tamagotchi Planet. Therefore, if you have been a excellent caregiver to your Tamagotchis, then you should not have any characters to view here.
