Is it a good idea to learn through the hydrolysis of each functional group separately? Will this be the best way, in the long run, of predicting the products of the hydrolysis reaction (or of an analogous condensation)?
I think any good organic chemistry course or method of learning will depend greatly on mechanisms and working out mechanisms - because mechanisms are the key to remembering and predicting reactions. The mechanism provide a logical analysis to why things happen a particular way and
not some other way. These are very crucial. If you compare and contrast different factors throughout your organic course and try to understand in which case what factor is important, I believe you can succeed in O-chem.
Having said that, there can be two approaches towards covering your course-work - both based on mechanisms. One approach is classifying reactions according to functional groups viz. reactions of Carbon-carbon multiple bonds, reactions of the carbonyl group etc. ; another approach is classifying reactions according to the reaction type- viz. electrophilic addition, pericyclic reaction etc. My personal opinion is that, I find the second approach more logical and helpful in the long run. Your course follows the second approach- classifying according to reaction type. That's good. I feel the problem with the functional group approach is that, for a beginner things get scattered and confusing. For example, one would find charged cyclic intermediates under the umbrella of Alkenes, Alkynes (reactions) , Epoxides (reactions) , Alkyl Halides ( preparation ) , and aldehyde-ketones ( preparation ). The same theme is repeated in 5 sections, possible more. If the beginner is shown the patterns and similarities in reaction of all these reaction intermediates in a single chapter on " Charged ring intermediates " , things will be more organized and less confusing- and above all more time-saving than repeating the same theme in different chapters.
However, I personally think that when you move on to synthesis, you will do better if you do your revision from a functional-group based book/ course-material. For learners, things should be organized and easier to grasp. Synthesis is like a puzzle and synthesis involves transformation of functional groups - and not reaction intermediates. Thus I feel, the functional group approach is more effective for synthesis.
I'd suggest a combination of both will be good, keeping in mind the limitations of both.