Will signing out of my Apple ID on iPad sign me out from my iPhone?

No.

Skylar_147 Said:

"Apple ID: Will signing out of my Apple ID on my IPad sign me out/mess up my phone?"

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Important:

90-Dat Redownload Wait: If you sign in with a different Apple ID, it may. This is because there is a 90 limit for redownloading items. So, stay on your Apple ID, unless you decide not to use your Apple ID for 3 months.

TheLittles is correct. I was forgot about that restriction.