Can you check the grammar in these two sentences, please? Thank you.

1) Best would be to know the name of the principal "and" the teacher who is designated with these programs; if I find that information I post it to you. 2) Addressing both would be considered as very polite and since you want something from them, pampering seems good.

Do you think an English mother-tongue speaker wrote them?

No, a native English-speaker did not write these!

1) It would be best to know the name of the principal, as well as the teacher who is designated for these programs. If I find that information, I will let you know.

2) [I'm not sure what you mean here. Please explain in more detail. For example, who or what are "both"?]

To check the grammar in the given sentences, let's analyze them one by one:

1) "Best would be to know the name of the principal 'and' the teacher who is designated with these programs; if I find that information I post it to you."

- The word "and" should be capitalized since it begins a sentence.
- The phrase "if I find that information" should be followed by a comma.
- The phrase "I post it to you" should be rephrased as "I will post it to you" for clearer future tense.

Corrected sentence: "Best would be to know the name of the principal 'And' the teacher who is designated with these programs. If I find that information, I will post it to you."

2) "Addressing both would be considered as very polite and since you want something from them, pampering seems good."

- The word "And" should be capitalized since it begins a sentence.
- The phrase "since you want something from them" should be followed by a comma.

Corrected sentence: "Addressing both would be considered as very polite. And since you want something from them, pampering seems good."

Regarding whether an English mother-tongue speaker wrote these sentences, it's difficult to determine solely based on these sentences. There are a few grammatical errors, but they could be made by someone who is not a native English speaker or by someone who made typographical errors. It's always best to ask the author directly for confirmation.