Our new house has two downspouts on the each side of the front of the house. They both at one time went into the ground which as I understand is the way they use to do this but is considered bad now.
Right. You want to get the rain water away from the foundation of your house so that there's no hydrostatic pressure driving that water into the foundation. Leaving that gutter to dump water into the flower bed like that isn't good. You want to get rid of the water further away from the foundation of the house.
A few months before we bought the house, one of these lines backed up due to tree roots and flooded the basement. The basement was repaired and the foundation was waterproofed in that area but the pipe the tree roots breached was not fixed.
You might want to hire a plumbing company to run a video inspection of that drain pipe to see if the pipe is actually damaged or not. If it is, you're going to continue having problems with tree roots until the damage is repaired.
You see, given the huge amount of buried sewer pipes and trees growing near them in cities, it's actually very seldom that tree roots grow into drain pipes. That's because drain or sewer pipes are buried a minimum of 5 or 6 feet down so that they're below the frost line and don't freeze in winter. Tree roots, on the other hand, only grow in soil that is fertile, and fertile soil is produced by the AEROBIC decay of organic matter like grass cuttings and leaves. Below about 2 or 3 feet down, you no longer have aerobic decay because there's not enough oxygen in the soil to support aerobic decay. So, regardless of the size of the tree, virtually all of it's roots will be within 2 1/2 feet of the surface of the ground. You might have a tap root or root ball directly under the tree that's a lot deeper, but anything more than two or three feet away from the tree, the roots will all concentrate in the top 2 feet of soil or so.
Where you have a crack in a pipe that allows moisture and organic matter to get into the soil deeper down, the tree considers that to be fertile ground too, and will grow roots into that soil. However, you have to have a sufficiently large leak in the pipe to get the tree to notice that the ground seems fertile in one particular direction or in one area. Small leaks several feet below the roots won't do that.
Before agreeing to buy the house we made the seller relocate this downspout. Their brillant solution was to redirect it into the small garden directly in front of the house. So the water wouldn't reach the foundation, they dug a trench with the heel of their foot in the garden which fills up with water when it rains which is obviously not ideal. The problem we're having is we can't figure out where to redirect this downspout as there's no clear path to the lawn. In that corner of the house, the driveway is on one side and the walkway to the front door is in front of the house. We thought about redirecting it to the driveway but the driveway is pretty level so the water would just sit there. We thought about buying one of those rolly things that rolls out when it rains but don't think it would roll itself over the retaining stones in the garden to get to the lawn. What would you do?
Dumping the rain water on the driveway is a bad idea. In the spring or fall when it rains during the day and then freezes at night, you're going to be parking on a skating rink.
If the problem is having the rain gutter cross the sidewalk, then if it were me, I'd probaby drive a tall cedar post into your front lawn close to the house, but on the other side of the sidewalk. Have the rain gutter go from your roof to the top of the post and then down to ground level so you can walk under the gutter.
Also any idea why the brick near the ground is a different color? Is it water damage? Is that nomal?
It's normal if you have a flower bed right beside the brick exterior like that. What happens is that when it rains, mud from your flower bed gets splashed up on the wall and discolours the masonary. It doesn't do any harm, but it does make the wall look darker in the vicinity of the flower bed. You'll find the same thing wherever you have those conditions: a porous surface that dirt will find it's way into right beside an exposed source of dirt like a flower bed.