Sorry, VI, that's not totally correct.
Verb patterns can be verb+ ing, verb + infinitive with to, verb + infinitive without to, verb + object +infinitive with to, etc etc. To throw an even bigger spanner in the works, you sometimes find 2 forms with different meanings: think of the difference between "I remember to lock the door before going out" and "I remember locking the door before going out".Subtle, but important!
If you google "verb patterns" you get the full list. It's one of my students' worst nightmares, trying to learn the rules when really it's just a matter of having to learn the pattern for each one as you come across it.
As I said before, both need+ gerund and need + infinitive are correct (as is need+ object + infinitive with to)
Need + gerund seems odd to us, because it's an active verb form with an inherently passive meaning. A true passive is subject+ to be + past participle of main verb. (the bread is eaten by the birds)
Wish is usually followed by a past tense/conditional verb phrase. "I wish I could fly" but usually with a present or future meaning. We use the past tense/conditional form to show its distance from reality, because English rarely makes use of its subjunctive anymore, unlike French, Spanish, Italian etc.