Chemistry - Can other substances be dissolved in a saturated solution?
Solution 1:
Saturating a liquid with one solute does not mean that the liquid will no longer dissolve another solute. However, you can expect the solubility of the second solute to be different, generally lower, than in the neat solvent.
One relevant concept here (though not specifically applicable to sucrose), in the case of ionic solutes, is the common-ion effect. According to this Wikipedia article:
The common ion effect is responsible for the reduction in the solubility of an ionic precipitate when a soluble compound containing one of the ions of the precipitate is added to the solution in equilibrium with the precipitate. It states that if the concentration of any one of the ions is increased, then, according to Le Chatelier's principle, some of the ions in excess should be removed from solution, by combining with the oppositely charged ions.
Regardless of whether the solute is ionic or not, when you are given a solubility value, for example, the solubility of some compound in water as $\pu{g solute/100mL water}$, this value is only relevant to the solubility in pure water. Once you have saturated water with sucrose, you then have a very different solvent system. There are no simple means of determining what the solubility of a particular solute will be in a solution saturated with another solute. However, there will, in general, be some solubility of additional solvents except as in the case described for the common ion effect.
Please don't hesitate to ask for clarifications in the comments below if I have misunderstood your question or left anything out.
Solution 2:
There is no such thing as saturated solution in general. There is such thing as solution saturated with (for example) sucrose, but that doesn't prevent it from dissolving anything else.
Different compounds may indirectly affect each other's solubility via water activity, ionic strength, common ion effect, and/or complex formation, but that's another story.
Solution 3:
Yes, it is well possible. Try this at home: prepare an aqueous solution of table sugar (maybe not one litre, you cup of tea may be, in terms of volume offered, sufficient). Then look out for table salt, add some, and stir the liquid. Does this solution saturated (in terms of sugar) dissolve any salt?
After this experiment, do not drink this "beverage". Rinse your cup of tea in the sink. Besides, the taste is repulsive.
There are instances where the presence of one substance (your solute, here: sugar) in the solvent (here: water) does not influence the solvent capacity for another compound to be accommodated. It may happen that the presence of A aids the solution of B in your solvent, increasing the solvent capacity for B. Conversely, the presence of A may lower the solvent capacity for B, too -- the experiment will tell you the ultimate truth.