Judging orders in a series of compounds
Don't worry too much about it, this educational exercise will be over when the exam is over. In real life nobody can predict the melting point or solubility in water just by looking at the structure of a given molecule. There are software like ACD, ChemDraw and SciFinder database which have predicted melting points and boiling points of most known compounds but those values are often off. Sometimes the values are correct. This is why only the experimental values of are considered reliable. Maybe in future, our understanding will become so much better that melting/boiling points and solubilities in water would be accurately predictable.
All your teacher wants is to remember some general trends and periodic properties, which should be in your mind (in other words memorize, just like 2+2 is always 4). Take the example of halogens (diatomic molecules). As you move down the group the melting point increases. Fluorine has the lowest melting point and iodine has the highest.
In the alkali metals, the melting point decreases down the group. All you have to keep in mind the melting point trends down in the groups as well as across the periodic table for simple molecules. Similarly, look for the trends in alkali halides, hydrogen halides, other hydrides of the oxygen group.
Read this article on Is there a trend in melting points on the periodic table? https://antoine.frostburg.edu/chem/senese/101/periodic/faq/melting-point-trend.shtml