Do Mobile Company Store Biometrics Taken at the Time of SIM Verification, and can it be used for any other purpose later?

No this is absolutely false, no one including mobile companies can store or use your biometrics which was taken at the time of Aadhaar re-verification. The biometrics are encrypted as soon as Aadhaar holder places his finger on the fingerprint sensor and this encrypted data is sent to UIDAI for verification.

Do Mobile Company Store Biometrics Taken at the Time of SIM Verification, and can it be used for any other purpose later?

Regulation 17(1)(a) of Aadhaar (Authentication) regulations 2016, strictly prohibits any requesting entity which includes mobile phone companies banks etc. from storing, sharing or publishing the fingerprints for any reason whatsoever and neither shall it retain any copy of such fingerprints. Any violation of this provision is a punishable offense under the Aadhaar Act 2016.