I think that thisis a good resource for programmers new to design patterns. There aren't distinct sections for the particular patterns you are asking about, but managers and factories do come up in various places.
I also think it's important to point out that they aren't exactly pieces of game engines so much as they are solutions to common programming problems. It isn't that game engines use a pattern in scenarios A, B, and C, but rather that games need to execute tasks often have needs that are met by patterns, like any other software.
For your specific questions, SmkViper has already provided good answers.