Bury downspouts plan

[stryker2000]

I'm trying to determine the best route to bury the gutters around this house. The sunroom has 3 around it and the ground gets saturated, which is the top left room in the picture. The bottom I have out near the sidewalk (orange line) but am debating just running all of them out towards the back since it's a small patch of brush with a street drain to the left (purple). There is also a downspout that I have coming out onto the driveway (bottom left picture). It would need to be routed under the sidewalk and out in the yard.

Can these be tied together as I have shown with pvc? I see some videos showing corrugated. Also, what are the best options in-yard for termination? I see popups around the neighborhood and they are just making puddles.

 

[stryker2000]

No ideas? I was thinking about getting someone to mark everything in the yard and then either hand dig or rent a trencher. But, I still can't figure what piping I should use. I was thinking sdr-35 and pipe the majority to the back. I'm also thinking about possibly taking the right side of the house to the back as well. That's a lot of water though.