Putting the brick on a sand base or directly on the ground is what will crack your joints. You want pavers to hold up, lay a 4" base of concrete with reinforcement down first, then lay your brick on a full mortar bed. Then fill the joints with mortar.
To lay on sand or earth, forego the mortar joints, and lay it tight joint, as iLikeDirt answered, and pull and spray the occasional weed. A mortared joint will not stay in place, freeze/thaw will see to that....
Here is a pic of my cousins sidewalk, done with a cement base as mentioned above. It has been in place for over 10 years. Long enough for the expansion joints to erode and allow weeds to grow through them. The placement of expansion joints are critical for the longevity of any concrete slab.
Option 1(clean finish):Rough cut the iron, bar the concrete, and pour a top layer of grout or thicker layer of concrete.
Option 2 (rough finish, what you're doing): Rough cut with rip saw and finish with grinder.
Option 3 (rough finish, completely removes visible pipe): Clear adequate space around the pipe below the concrete for a cast iron pipe cutter
You're going about it the right way.
Option 2 details: Depending on your comfort with a rip saw, you may want to start with a masonry grinding wheel to smooth ~4" of the concrete around the iron to minimize risk of kicking against exposed stones (aggregate).
Using a medium gauge cutting blade(https://www.lowes.ca/reciprocating-saw-blades/lenox-es-2017-14-tpi-lazerreg-metal-cutting-reciprocating-saw-blade-5-pack_g2347551.html?searchTerm=lenox-lazer) trim off all that you can comfortably trim, follow up with a cut off wheel (https://www.amazon.com/Walter-ZIP-Cutoff-Wheel-Pack/dp/B00NFHM9E0)
From the 18" that you mentioned, this should take around an hour with out breaks. You'll need roughly two discs and two blades.
Option 1 is significantly more expensive and time consuming.
-Start by deciding whether you'll use grout (minimizes the profile[depth]) or concrete, if you're using grout there are specifics that need to be considered, if you're using concrete, it's straight forward, minimum 2" pour.
-After you've decided which (or any other local option) you're going to use, use a rip saw, (or as another has suggested, a torch) to clear the pipe from the surface, leaving it partially exposed doesn't matter, as long as you can have it completely enveloped by the concrete.
-Depending on the state of the slab, and your weather, you'll want rebar spaced at around 16" square from each other, figure out how much you'll need based off what you're expecting to add (min 4"), purchase re-bar and structural epoxy or grout.
-Mark off and drill the holes based off of what you're inset is (min 3") again at 16" square (more or less based off your weather)
-Pressure wash the surface, and clean out the holes from all dust, and sitting water
-Set the re-bar in to the holes with the grout or structural epoxy while waiting for the compound to cure/set...
-Frame off the slab for the pouring of the concrete and making sure it's moist but no sitting water (if it's grout, there can be sitting water for concrete) and finally perform your pour.
There isn't any more guidance that I can provide for this option, it can vary wildly based on what your local weather, building materials, expectations of quality, and more.
Option 3 can vary depending on the thickness of the slab, it can be time consuming, and requires renting of any tools you don't already have (SDS, SDS bits, cast iron pipe cutter). Again I can edit and provide more details.
Best Answer
Concrete obtains its strength due to the cement-water ratio. This means water is not a "relative" thing, but critical, in fact.
The fine and coarse aggregate (sand and stone) are basically just fillers. The space in between the aggregate needs to be filled with cement paste (cement and water). The more paste, the more cement you need.
A concrete mix design is based on the principles mentioned above. Depending on the source of your aggregate, your cement paste requirements may vary.
The "rule of thumb" ratios are based on experience, but don't guarantee a particular strength concrete.
A nice source of standard mixes for various requirements can be found at the South African Concrete Institute website