Can anyone identify a weed and a fungus?!?

I have the weed growing in my garden, I'm told be a neighbour that it's one

of these "superweeds" whose roots will eventually lift my patio and make
my 
house fall over. Any ideas what it is, and how to kill it? I've tried 
spraying it with weedkiller, I've drilled down the main stem and filled it

with weedkiller but it still comes back and I don't have enough room
between 
patio and fence to dig it out or burn it.

The second problem is a fungus that's growing on a wooden bench, any tips 
how to get rid of this would also be appreciated.

Thanks!

weed: http://i29.tinypic.com/68tvug.jpg

fungus: http://i28.tinypic.com/24vobyp.jpg