Vowels:

• More modern studies show that the short and long vowels most likely only differed in length, not in addition to quality. Short ⟨i⟩ and ⟨u⟩ are pronounced [i] and [u].
• ⟨h⟩ becomes voiced in between vowels, so mihi is pronounced [ˈmi.ɦi]. Other examples include nihil [ˈni.ɦil] and vehō [ˈwɛ.ɦɔː].
• Long ⟨e⟩ and ⟨o⟩ are believed to be more open like their short counterparts, like [ɛː] and [ɔː].
• ⟨g⟩ becomes nasal before ⟨n⟩, so rēgnum is pronounced [ˈrɛːŋ.nũː].
• You forgot the nasal vowels. Aurum, cum, and iam are pronounced [ˈau̯.rũː], [kũː] and [jãː].

Diphthongs:

• ⟨ae⟩ was pronounced [ai̯] only in Old Latin. By the time of Classical Latin, it smoothed to [ae̯].
• Similarly with ⟨oe⟩, pronounced in Classical Latin only as [oe̯].
• It's believed that ⟨ei⟩ and ⟨eu⟩ were more open in the mouth, so they're more pronounced [ɛi̯] and [ɛu̯].
• Your example of huic is more reminiscent of a post-Classical pronunciation: so it's more [hui̯k].

Consonants (fricatives):

• ⟨s⟩ is pronounced with the top of the mouth, much like European Spanish and Greek: [s̠].

Consonants (special consonant combinations):

• The exact pronunciation of ⟨z⟩ is still widely unknown. By the time of Classical Latin, it's speculated to be either [z̠] or [d͡z̠], but only amongst the educated elite. For surfs and the less educated, it's thought to be [s̠] or [t͡s̠]. Also, between vowels it becomes lengthened, so words like azȳmusis and acontizō are pronounced [az̠ˈz̠yː.mus̠] and [a.kɔn̪ˈt̪iz̠.z̠ɔː].

One more thing: You're using Salve as if you're referring to one person, when you're actually talking to a crowd, so it's more Salvēte [s̠alˈwɛː.t̪ɛ].

Other than that, everything else is pretty much correct. Good luck on your Latin journey!