Mould, damp and uninvited plants

[coaster8]

Hi all,
This might sound strange but for some reason there is a plant growing out of my window sill. I have been living in this house for five years and a few months ago a plant started growing directly out of the window sill which is very strange as I haven't planted anything. Beneath this window, the wallpaper has started peeling off and mould has started to grown on the walls. I will remove the plant today but wanted to ask if anyone knows what plant this is, how to fix the mould on walls and how to prevent this plant from growing again. Thank you so much in advance

Do you remember throwing your magic beans out of that window?

You have a wet wall. Stand back and take a pic of the wall. All the way up to the gutter, and down to the ground. Include all downpipes and drains, bay windows and their roofs, and windowframe junctions with the wall.

Inside and out.