How to create pitch/slope in a cured cement slab??

This can be a complex fix - which you've learned. I would call in several experts and have your husband "play dumb" while wringing them for info.

Hello. Gosh this looks like a frustrating and complex situation. One question I wanted to ask was are your gutters buried and extend it out into your yard? If they just end at your foundation line the excessive water running off your roof could be impacting this situation greatly. Something to think about.

To Vim's point, where is the water coming from? You mentioned the walkway is pitched downward from the street to the house, but the new slab raises it up a step. It looks like your lawn is below or level with the walkway. Is water coming off the roof? Down the walk? Running in from the yard? Where does the French drain drain to? Need a little more info to give you a more specific solution.

I found this and it looks like a lot of work, but my be worth it and a good solution for your problem: https://www.youtube.com/watch?v=D1IvGH-gUDY

Get some gutter extensions at Lowes or HD. That will greatly ease the water problem. Other than that you may need a contractor to fix the added slab problem. Sloping is extremely important and it may need to be redone. A mess I know.

If he forgot to slope the French drain sufficiently, then excavate it and change that.

Is the slope of the new concrete pad also not sufficient? Can you grind drainage lines or a chamfer edge with an angle grinder?

Yes, check your gutter's slope.

I've had to abandon the under-ground downspout drain systems on my past two houses.

Your property needs to be able to handle the amount of stormwater and rainfall it receives, so extra water doesn’t cause costly damage.

There are a variety of solutions, depending on the exact problem and the characteristics of your property.

Sometimes, a combination of solutions is the best plan.

Here’s a look at some options:

This is a subtle and creative solution for backyard drainage issues that offers a bonus: it’s pretty.

A shallow trough is lined with stones or rocks, offering excess water a place to flow and runoff.

This is a great choice for heavily paved areas, such as walkways and parking lots. Trench drains are concrete-lined channels that help direct water flow while filtering out debris using grates or filters to reduce clogging.

One of the more intricate methods of controlling water flow around a building or property is by using French drains.

These are typically perforated pipes that channel water in a specific direction. These pipes are usually covered with rocks and gravel to help with filtration, water flow and ensure that the pipes stay in place.

French drains are the go-to choice for preventing flooded basements.

Site grading involves changing the landscape to encourage water to flow in the desired direction — away from the house.

Many drainage issues stem from improper grading techniques during a home or building’s construction.

When surface water has no place to go, it pools and floods. Building a dry well underground, or a reservoir on the surface gives excess water a home.

I found this info for you

https://www.doityourself.com/stry/how-to-slope-a-concrete-patio-for-drainage

https://www.hunker.com/12598284/problems-with-concrete-patio-drainage

What if you cut a small trench between the brick & slab? Then you will have a way for the water to escape.

You can grind concrete with a angle grinder and a diamond disk..

this may help https://www.nachi.org/roof-slope-pitch.htm

You have many different materials and surfaces, some of which appear to be trip hazards due to the gaps and drop offs. The fact that the ledges and heights do not match up is certainly not the safest situation to have near steps. It also appears that the entire brick step area is sinking and shifting.

The answer is not to continue trying to add more materials in attempt to patch up individual areas. This will only intensify the retention of water and erosion of the earth under the concrete and bricks.

The solution is to tear everything out, have the entire area regraded and new concrete, or paving stones installed.

I agree with Flipturn. The more you add, the worse things are going to get, especially if slopes are missing and more impervious materials are added. While it'll be a pain, ripping it out, re-grading, and starting over is really the only true solution.

I would contact a repair person

How about Duckboards!

If you can imagine a Pallet only smaller scale on the ground allowing you to walk through water without getting your feet wet!