When should verbs follow pronouns?
This is something I've been confused about. Why do the verbs in the following phrases follow the pronoun?
Il me voit
mois me lave
Edit: Thanks to everyone who answered! This makes sense to me now. :) And I fixed the last phrase. Bonne journée !
"Je me lave." The direct and indirect object pronouns usually precede the verb in French, except in the imperative mood. Now, what I mean is that they precede the conjugated form of the verb in compound verbs, but it goes in front of the infinitive that it applies to rather than in front of a modal verb. So you have " Je t'ai compris." (I have understood you) but "Je peux te voir." (I can see you) and J'aime le faire." (I like to do it.) https://www.thoughtco.com/french-object-pronouns-1368886
Now "moi" is a whole different story. It can be used with prepositions, but it can also be used as a stressed pronoun.
There are verbs that require a preposition and so cannot take a pronoun in front such as "penser à", "songer à", "faire attention à" and "s'habituer à". We use prepositions in English too: "I think about that." Je pense à cela.", but in French you can replace the whole prepositional phrase with the adverb "y" which would be "J'y pense."
So the exception is the imperative mood, "Prend-le!" (Take it!) or "Donne-le-moi! (Give it to me!) https://www.thoughtco.com/introduction-french-imperative-mood-1368858
Oh, and "Je me lave." is reflexive and those pronouns are different when you get to third person "Il se lave." https://www.thoughtco.com/french-reflexive-pronouns-1368936
Then there is more than one way to ask questions in French and one way is called inversion in which the subject comes after the verb: "Voulez-vous danser avec moi?" Even another way to ask "Est-ce que vous voulez danser avec moi?" has "ce" after "est". This is not so hard for us to understand as we say "Do you want to dance with me?" and "Do" comes before "you". I have not seen inversion done with reflexive verbs though. People would ask "Est-ce qu'il se lave?" Even with regular verbs "est-ce que" form is used with verbs that have direct objects or indirect objects. https://www.thoughtco.com/questions-in-french-1368935
Ignoring the last one, all of the pronouns in your examples that are positioned between the subject pronoun and the verb represent direct objects.
As in English, a direct object is a noun or pronoun that receives the action of the verb directly, without a preposition.
Je t'aime → I love you
Il m'appelle → He calls me
Il me voit → He sees me
You last one, "Je moi lave" is incorrect. It utilises the reflexive verb se laver so should be Je me lave → I wash myself. This uses a reflexive pronoun.
For more info see: https://www.duolingo.com/skill/fr/Pronouns
There is the deep question of how languages with a common ancestor ended up with different syntax. A quick google search yielded: https://benjamins.com/#catalog/books/cilt.305/main