The contract must be verbal, and therefore texting will not be valid. As for a verbal phonecall, as long as all other conditions and requirements are met, it will be valid.
You have mentioned the essential requirements, and reciting it in Arabic formula is not a must. As long as the due purport is said, in whatever language.
Of course, something that was not mentioned is the female being from Ahlul Kitab, her having consent from father if virgin, and other details mentioned in practical book of laws.
Furthermore, the female is the one who initiates the contract, and the male is to accept.
Mut'ah marriage is a way to save people from falling into sinful acts but such type of marriage has conditions which must be fulfilled. If you need to save yourself from falling into sinful act through going for Mut'ah marriage, you need to get your Muslim wife's permission if you want to do the Mut'ah with a woman from People of Book (Ahlul Kitab) like Christians or Jews.
If the woman of the Mut'ah marriage with your husband is from People of Book (Christian or Jewish), then such marriage needs your permission.
If she is a Muslim woman, then her rights are not like your rights. Mut'ah marriage wife has no right of livelihood expenses, nor the right of spending nights with her like your right as a permanent wife. She also has no right in inheritance from your husband.
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