Re: Hole in pool wall
Welcome to TFP!
If you are sure you have all the roots out of the cracked and broken area, I think you can repair that.
You will need to get enough hydraulic cement from your local masonry supplier. A good thing to help with the sealing of the holes would be what I've always known as concrete bonding agent -- a white milky fluid you paint onto the surfaces of the concrete you are repairing.
For the larger deeper holes, you can use a sand topping mix, essentially a sand and portland mix. Add just enough water to make a loose mortar then fill the spaces to within 2" of the surface. Complete the repairs with the hydraulic cement, then replace the lost tiles.