Here's the other side of the deck/slab. As you can see, the grade is below the slab here as well, although only about 2-3 inches. The slope of the lawn as it comes down towards the slab is fairly steep, more than it looks in this photo. I could of course just add topsoil to raise the grade along the slab here as well, but my concern is that water running off that slope is going to wash over (or under) the slab, or just slowly erode the soil and put me back where I started. Instead, I was thinking about putting in a low retaining wall along that edge, only one or two courses high plus a capstone. Then I can backfill with some gravel and put in a perforate drainage pipe sloped away from the house that exits into the lawn just past the landing at the bottom of the deck stairs, to get the water running off that slope out around the slab so it can run off with the rest of the lawn. Or maybe I don't even need the drainage pipe, as long as I grade the lawn behind the retaining wall to slope very slightly away from the foundation?

From what I understand, you should probably remove all the plants to be able to get in there, add enough top soil and make the perfect slope. It should require stakes, rope, and a little bit of math skills to do so. Plus some plants really do not like to have soil added up on their stems, as it can introduce pathogens to them. This is entirely species specific. I also have to do this in my backyard - but I am going to hire a professional to get it right. It was DIYed by original owners of the house and much of the soil eroded away or settled. It will cost some bucks, but it is worth it to not have a leaking basement. I removed all the vegetation myself to save a bit on labor. From what I have read, landscape fabric is not advised anymore as it adversely messes with soil microbes beneath it. Plus, if you want to add plants later, you have to dig down deep enough and cut a hole in the fabric. I have planted plants in areas, not knowing there was landscape fabric underneath - no bueno - what a waste of money and time! Some people will disagree on this, as it will cut down on some, but not all, things from growing in your beds. For example, weeds with shallow root systems will still be able to grow in your beds. So as a newbie, I would gently suggest this, get some quotes for regrading and ask how you can save on costs (maybe removing the plants yourself won't save you much). If that fits in your budget, then you can DIY afterwards by adding the soil amendments (the regrade fill is likely to be far from excellent for your plants), plants and/or sod. Mulching any beds can help you build up the quality of your new soil, reduce water loss, and help prevent weed growth.

Your thread title wasn't very interesting but your problem certainly is. It is much better to have terraces on steep hills as you thought but with established trees you can't scrape up the roots on one side and bury them on the other and expect good results. If you were cutting through a lot of roots when you pulled soil from above that would have been your clue to proceed very gradually over several years. A few inches of mulch would have accomplished much of what you were trying to do anyway. If the lower roots haven't been buried too long you may be able to uncover them to original level and cover with mulch and pray to the citrus god for forgiveness. Unfortunately, according to citrus god laws, ignorance is no excuse. I don't think the acidity of the peat moss would much affect the pH of the soil beneath but it is not the best mulch to use unless your soil is excessively alkaline. Even in that case I'd mix it with something that stops and holds water like arborist wood chips.

Water flows downhill. The property has to be graded to make that happen. The water has to have an approved location to flow onto. That’s a different story. You may or may not be allowed to direct the water through a neighbors property or onto public areas. Your city engineer should have that info.