Mi cuello está mojado.

mi is a possessive adjective that you place directly before a noun (just like “my” in English). It never changes form.
mío, on the other hand, is a possessive pronoun (“mine”) that replaces the noun or follows it with an article:
• Es mi libro = It’s my book.
• El libro es mío = The book is mine.

Spanish has two verbs for “to be.” You use ser for permanent traits or identities, and estar for temporary states or locations.
• Mi cuello es largo (“My neck is long” – a describing trait)
• Mi cuello está mojado (“My neck is wet” – a temporary condition)

Yes. In Latin America, tener + noun + adjective often expresses a state or physical condition:
• Mi cuello está mojado emphasizes the current state (“my neck is wet right now”).
• Tengo el cuello mojado can emphasize that I “have my neck wet” as a condition or result, especially after you’ve just done something (e.g. “I just got my neck wet”). Nuance is small; both are perfectly natural.

Yes. Mojarse can be reflexive when you talk about getting something wet unintentionally or by your own action.
• Me mojé el cuello = “I got my neck wet” (I accidently wet it).
This focuses on the action/event (I got wet) rather than simply describing the resulting state.

They all relate to wetness, but differ in intensity:
• mojado = wet (water on the surface)
• húmedo = damp or slightly moist (less water than mojado)
• empapado = soaked or drenched (extremely wet, water has penetrated deeply)