It isn't clear - to me at least - what "general rules" you are talking about. Density is simply defined as mass divided by volume; this applies to any substance.
The exact material, amount of other substances (impurities) (for example, water moisture, in the case of air), the temperature, the pressure (which, in case of gases, affects density).
In general, an object floats if it is less dense (has less density) than the water (or other liquid).
As the temperature increases, the molecules gain more energy, and they move faster. As a consequence, they tend to move farther apart from each other thus taking up more space/volume. Density is the mass/volume. Since the mass does not change, and the volume increases, the density, in general, will decrease with increasing temperature.
The general rule is that an object will float on water - or on any other liquid - if it has less density than the liquid.
Hot air balloons heat up contained air so that the density of it becomes significantly less than the outside air and thus the container (balloon) will rise of float in the surrounding air until the density difference is null. Buoyancy is just that, less dense substances floating or rising in more dense substances. The other approach is saying more dense substances sink in less dense substance.
It is for some substances and not for other substances.
specific gravity
Some substances look alike and the density can help you determine which is which. It also helps to tell which is heavier than the other.
Difference substances may have such a density. Among other things, many rocks, such as basalt, may have a density in that range.
One is a unit of volume, the other is a unit of mass, so there is no general conversion. You can convert in the case of specific substances, if you know the density of the substance.
Density can tell you how "pure" a substance is. Since each substance has a specific density in its "pure" state, having no other substances in its composition, by measuring it density you can tell how pure the mineral or substance is, 99.9% pure gold.
If the substances in question remain in the form of separate layers, rather than dissolving into each other, then the densest one will be on the bottom, and with progressive height in the test tube, you will get progressively less density. Denser substances will fall through less dense substances.
Density is specific for each substance. Also the measurement is generally simple.
An egg will float in anything with a density greater than an egg.
The density of a substance is its mass per unit of volume. Density will be in units of mass (i.e. grams, kilograms, milligrams, etc.) over volume (cubic meter, cubic foot, liters, milliliters, etc.) For example, the density of water at 20 degrees Celsius is: kg 998 ----- m3
Generally not. The general rule to go by is like dissolves like. Polar substance will dissolve other polar substances while nonpolar substances will dissolve other nonpolar substances.
You can, but only if you know the density (or specific gravity) of the steel. Since steel is an alloy, its density is variable - depending on the other substances and their proportions in the alloy.