She got an email to pay the Turbo Tax fees?  Were they supposed to come out of her refund?

Sounds like the IRS is taking too long to send your refund or reduced it.  See What if the IRS reduces your refund or delays it.

https://ttlc.intuit.com/community/payments/help/what-if-my-federal-refund-isn-t-enough-to-cover-my-t...

Then when the IRS does send your refund they won't take the fees out again.

And, Why you got charged,

https://ttlc.intuit.com/community/charges-and-fees/help/why-was-my-bank-account-auto-debited-for-tur...

You should have received about 4 emails asking for the fees.  If you don't pay they will debit your account.  You had to agree to it.

The email what she got is a “Automatic debit“ email.Also me and my mother tax refund cannot find any information on the IRS ,“We cannot provide any information about your refund.”

The IRS is taking a long time to pay refunds.  They are very behind.  More people are filing returns this year to claim the Stimulus checks.  So you have to keep waiting.  The Refund Lookup page is delayed.   But you still need to pay the Turbo Tax fees.  

When will you get your IRS refund
https://ttlc.intuit.com/community/refund-status/help/when-will-i-get-my-irs-tax-refund/00/25589

IRS Refund FAQ
https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions