No, it hasn't -- muSwI' "a hater" is treated here as a new word to be learned as a unit.
The verb suffix -wI' will be introduced properly later on in the "Agents" unit.
If you're curious -- it forms agent nouns ("thing that does" or "person who does"), a bit like -er in English (a computer is a device that computes, a toaster is a device that toasts, a speaker is a person who speaks, etc.).
I am courious as to why this takes Haters hate as the right answer even though all the other words are avalible to click for the answer, yet in a previous one when you put the answer They admire instead of They admire her the system marks it wrong --yet there is nothing that tells you it is a he/she/it other then it being in the clickable options. Is it just a fluke of the system
Klingon does not indicate tense in the form of the verb. muS could mean "they hate", "they hated", or "they will hate". We also have a more casual future tense in English where we use "going to", so you could also translate it as, "they are going to hate." Since there is no context to indicate which tense is intended, the system accepts all the possabilities. So even though the system might have expected you to put the sentence together as, "Haters are going to hate," it must also accept, "Haters hate," since that is a possible meaning.
In the other exercise that you are referring to with luHo', "they admire" is not a possible translation. The lu- prefix requires you to mention a grammatical object. If it only offers you one of the third person singular object pronouns, then you must choose that one. If it offered you all of the tiles, "him", "her", and "it", then you would get your choice of which you wanted to use, but you would still have to choose one of them or you would be marked wrong.