There are trowel on moisture barriers, but a glue on pad??? Beneath grade? Wood and laminate really are never successful below grade when there are moisture issues. This sounds like a non standard installation. If you drive that glue into the slab by using solvents, you run the risk of not having tile stick to that slab. Or anything else. A floating floor may be the only thing that's left you at that point, and again, even with your moisture issue "corrected" you may have issues with those below grade. You REALLY need an expert in there at this point. One of those flooring removal machines first, and then something to sand off the top layer that's contaminated with glue will be needed. If you've already contaminated the concrete further than just the top layer, you may have to remove the slab entirely and repour if you want tile. But, at least that approach would give you the opportunity to address the moisture issue properly from the ground underneath the floor up.

We did something similar. We didn't lay tile, and although the patio was your typical small one that comes with most houses, we wanted a much larger area attached to it. There was also a sidewalk we had to incorporate into the design. No concrete matched any concrete due to stains and age differences. We hired someone to pour a new concrete patio next to the existing sidewalk and old patio. Then someone else came and painted all the concrete light gray, laid strips of tape to form stones, used 3 colors of stain, lifted the tape, sealed it all, and it is gorgeous! One big flat patio! Our job totaled $10,000 here in Southern California. Here is the ugly stained patio and the sidewalkHere it is after the work And here is the long view of the entire thing:

How large is a "fine crack"? A photo would be helpful. The saw cuts are control joints that do not go all the way through the slab and are intended to encourage the inevitable cracks to form there instead of elsewhere. An expansion joint is a separation between slabs to allow differential movement. Its impossible to know if the slab was poured properly but I suspect a high water content, poor curing efforts, insufficient reinforcement, or hot/dry/windy weather. If this is essentially a cosmetic issues, it should only matter if the slab is exposed.

PPF: All materials have a coefficient of linear thermal expansion. Coefficient of linear thermal expansion for concrete is roughly the same as for iron which is why it (rebar) works well with concrete. Expansion/contraction is significant for long linear surfaces such as the large concrete slab with the crack OPs thread. Though there is a much more to material science, especially concrete and types of concrete, hopefully the following excerpt provides an adequate explanation. THERMAL EXPANSION AND CONTRACTION Materials expand or contract when subjected to changes in temperature. Most materials expand when they are heated, and contract when they are cooled. When free to deform, concrete will expand or contract due to fluctuations in temperature. The size of the concrete structure whether it is a bridge, a highway, or a building does not make it immune to the effects of temperature. The expansion and contraction with changes in temperature occur regardless 0of the structure’s cross-sectional area. Concrete expands slightly as temperature rises and contracts as temperature falls. Temperature changes may be caused by environmental conditions or by cement hydration (the exothermic chemical process in which the cement reacts with the water in a mixture of concrete to create the calcium silicate hydrate binder and other compounds). An average value for the coefficient of thermal expansion of concrete is about 10 millionths per degree Celsius (10x10-6/C), although values ranging from 7 to 12 millionths per degree Celsius have been observed. This amounts to a length change of 1.7 centimeters for every 30.5 meters of concrete subjected to a rise or fall of 38 degrees Celsius. Thermal expansion and contraction of concrete varies primarily with aggregate type (shale, limestone, siliceous gravel, granite), cementitious material content, water cement ratio, temperature range, concrete age, and ambient relative humidity. Of these factors, aggregate type has the greatest influence on the expansion and contraction of concrete. Severe problems develop in massive structures where heat cannot be dissipated. Thermal contraction on the concrete’s surface without a corresponding change in its interior temperature will cause a thermal differential and potentially lead to cracking. Temperature changes that result in shortening will crack concrete members that are held in place or restrained by another part of the structure, internal reinforcement or by the ground. Forexample, a long restrained concrete section is allowed to drop in temperature. As the temperature drops, the concrete tends to shorten, but cannot as it is restrained along its base length. This causes the concrete to be stressed, and eventually crack. Joints are the most effective way to control cracking. If a sizable section of concrete is not provided with properly spaced joints to accommodate temperature movement, the concrete will crack in a regular pattern related to the temperature and restraint directory. Control joints are grooved, formed, or sawed into sidewalks, driveways, pavements, floors, and walls so that cracking will occur in these joints rather than in a random manner. Contraction joints provide for movement in the plane of a slab or wall, and induce cracking caused by thermal shrinkage at preselected locations. One of the most economical methods for making a contraction joint is by simply sawing a continuous cut in the top of the slab with a masonry saw.