Yes, you can refreeze everything if only the qualities are being ignored. I'm not sure about the milk's quality/freshness after thawing a refrozen thawed milk. Please don't refreeze anything without cooking it, see this: http://www.hertspartsft.nhs.uk/_uploads/documents/the-trust/trust-papers/policies/health-and-safety/foodhygiene.pdf
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You can, but its shelf life will have been reduced. By how much will depend on how long it has been at room temperature. If it has been out more than 2 hours, you might consider discarding it. Do not mix it with refrigerated milk. Doing so will shorten the shelf life of the colder milk.
Yes you can but it will not take but a day to spoil in the refrigerator. Milk is one of those foods that you have to be careful with. Try not to refrigerate heated milk often.