Hello,
The first one is onion weed and the second one sounds like Wandering Jew, this can be a big problem. It is difficult to get rid off and can be a problem for dogs as they can get sores and skin infections from it. Our garden is unfortunately like a demonstration garden for every obnoxious weed on the list! The banana passion plant is another favourite.... As are jasmine, clematis etc. I never thought I would be pulling up nasturtiums by the armful and cutting down jasmine.
Here is a very helpful guide to what is considered a pest plant in NZ:
http://www.biosecurity.govt.nz/files...ord-manual.pdf