The Valar and Men

Having read LOTR a couple of times and having some exposure to the other related materials, one thing seems to always make me scratch my head – the relationship between the Valar and non elfish races of ME. It just seems that the Valar would be hard pressed to care less about the struggles of other races. I know that they held the elves the most dear, but was there even much thought to condition of the other races? Are they not the protectors/overseers of all of ME? All of this leads me to series of questions –

Could they not have handled the Numenorians themselves or why did they feel that they must turn to Eru, especially since they handled the Morgoth situation?

If the elves had just come over the seas and not tallied in ME, therefore not exposing themselves to Morgoth’s evil, would there ever have been a war of wrath?

If Sauron had reclaimed the ring, and the remaining elves had safely made it off ME, would the Valar have done anything about his terrible reign or figured “oh well”?

Did they grieve for the losses suffered by all races or was it - lose a 100 elves, terrible – lose 10,000 Men, sh*t happens?

If they did not have a great love for Men, was it bound to jealousy in that Men were not bound to ME, while they must remain in it till the end?

If they envied this gift of death, did that play a part in their actions toward the mannish races?

Was the inaction of the Valar in the third age purposefully done due to other reasons than just because most elves were already with them safe in Aman? (And would they have reacted differently if many more elves had been at risk?)

Were they really guardians of ME or just guardians of elf kind?

As stated above I am not a Tolkien expert and some, if not all, of these have probably been debated in other threads. They are just some questions I have in reconciling how the races of middle earth were held in relation to the Valar. Maybe I am wrong in some of my points, but whatever answers anyone can give would be helpful.

Thanks