In Software Sources under the Other Software tab, there is an option of enabling "Canonical Partners" repository: software packaged by Canonical for their partners.
Do I understand correctly that this repo includes third-party created applications that by arrangement are packaged and maintained by Canonical?
Does this mean Canonical can look at the source code of these third-party applications and hence ensure the security and stability of these apps in Ubuntu, making them as secure & stable as the software in the Main repo?
The Canonical Partner repository contains closed source third party software that doesn't cost any money. Canonical doesn't have access to the source code, they just package and test it and may provide feedback and help to the author if there are issues.
In addition to what said by @Florian, you can browse the content with Synaptic Package Manager