how often do private military soldiers get to go home ,?

Contractors get whatever time off their companies gives them in their contract.
Generally, the high paid westerners (Americans, Brits, etc) get some sort of R&R at least once a year. The low paid guards from third world countries might not get any time for vacation. I had some African guards in Iraq that had been there for 2 years.
As for taxes, you are talking about the finer points of tax laws from dozens of countries. Most people have to pay taxes to whatever country they are a citizen of, but there are always loopholes. They may have to pay taxes to the country they are working in too. Most likely they aren't paying taxes to the country where there company is incorporated though.

All soldiers get 30 days paid leave per year.

They pay taxes to their homes of records in the states. They do not pay host country taxes for income as they are exempted under the Status of Forces Agreements (SOFA) pertaining to their host country.

Pretty much every day, unless they are on an exercise. In my 25 years of full time service, I was deployed or away for about 3 years all put together. Otherwise, I was home.

And, yes, we pay taxes! When in a different country I believe we pay the taxes to the home country, as if we lived in the capital, so, federal, and provincial taxes too.

contractors can take leave as they earn and as their company allows. the cost of getting home (out of theater) and back is ON THEM. they really don't have R&R.

as far as taxes, that is tricky. it depends on their deployed location and how long they are there. for example, if contractor is in afghanistan (and this is where i met my husband), they have to be in the 'tax free exclusion area' for 330 days of a contract year. if that is true, the first $95,000 (i think that is the maximum, i'll have to ask the hubby) is tax exempt. anything short of 330 days, it is prorated, and you have to be REAL CAREFUL where you go on leave. if you go back to the states for a month,....gets tricky.

that is for FEDERAL taxes, and it doesn't apply to all areas. if you deploy to germany, you'll have federal taxes withheld. japan? as i understand it, you'll pay taxes. Kwajalin? no taxes. it all depends. would probably have to google it.

STATE taxes is going to vary by state. I am a Texas resident, i don't pay a personal income tax and none is withheld from my check. My husband maintains a residence in Florida, they don't have a personal income tax either

whats a private soldier ?

there is no such thing