It’s a good idea for him to learn Cantonese. (learn) is the base verb, but in this context we need the infinitive form to show the action he should take.
Life has become more convenient thanks to Internet and social network. (convenient) is an adjective describing life, so we need the comparative form (more) to show the increase in convenience.
They had better choose more exciting music for the party. (choose) is the base verb, and since it's a suggestion with "had better" we don't need to change it.
If you want to volunteer, there are endless opportunities for getting involved. (endless) describes the number of opportunities, and "endless" emphasizes the vast amount available.