An unappealing mixture of many things... a hodgepodge... a disorganzined mess... but probably still usable (or consumable in the case of food.) From the idea that a dog will eat anything and feeding it a mixture of whatever is on hand. (Unappealing because only the dog finds its breakfast appealing... if you see or smell the dog food in the morning, as you're feeding the dog, it may well turn your stomach.)
Those contractors didn't do very good work and the made a real dog's breakfast of that job
I have no idea of the origins of this word, so my understanding of it may be wrong, but where I come from its a phrase that means you're so completely tired that you're over tired or totally beat. I can only hguess its a reference to the fact that a lot of dogs seem to sleep a lot and thus appear to always be tired and in need of sleep.
The obvious definition is that you did one thing, which led to a situation where it was logical to do some other related thing.
It can often be used to say something without actually saying it--you might say the phrase to imply that something happened which you are not going to be explicitly explain... (see the example below.)
I heard this rumour about John and Beth: Beth invited John to dinner last week, during which he accidentally spilled wine on his pants. Beth told him he better take them off so she could clean off the wine before it made a permanent stain. I guess John got a little aroused by the situation, and one thing led to another...
A brass monkey is a naval term for the holder that holds the cannon balls. It was made of brass and the cannon balls were not, so when it got cold enough, the two metals would contract by different amounts and the cannon balls would no longer fit properly in the holder and thus fall off.
Person 1: Holy crap its freezing in here.
Person 2: Yeah, its cold enough to freeze the balls off a brass monkey.