[Nealtw]

The low spot in the back your should have been out at the bottom of that slope. with 2 drains to move water

Do you have a basement?

 

[Nealtw]

Yes, I have a garage and a basement that are essentially "under ground" from the perspective of the backyard

Like Paul said , If you raise the dirt level you will want to waterproof what will be below the new dirt level.
Is the foundation full height behind the brick.

 

[Nealtw]

I was going to ask what you would do with the deck but I notice that it is attached to a bump out, that is against code it should be free standing close to the wall.
Se how it should be framed but 6 ft is the max for the bump out.

Your plan is not bad, you would want the dirt to stay 8" below the level of the sill plate inside sitting on the foundation.
I would run 2 pipes, one solid for the downspouts and one with holes to gather water.
Adding both in one pipe would just allow roof water to go into the dirt.