Hi All, new member and new to gardening in general!

I have a small problem - To the back of my house there is a playing field surounded by trees, a few months back the counsel arrived and cut down every second tree (by the looks of it) these trees are about 10ft from the boundery of my garden.
Sence the tree has been cut, my avarage size garden has been sprouting small tree roots, there a nice covering over the whole garden, i would guess there are about 50 or so.

So, advice needed. but I do have two questions...

1- im guessing the trees roots are heading towards my house, is there any chance of future damage to the foundations?

2- to remove them whats best - cut, pull, lawnmower or none of these?

Cheers all!