when creating a new wallet, how do the Blockchain network check if a certain mnemonic seed phrase has been used before for creating another wallet?
The network doesn't check previous usage of the seed.
If you're importing a seed into a wallet and the wallet automatically imports used accounts generated from this seed - this check is performed on the wallet level.
It keeps iterating the index number in the derivation path - each iteration results in one account. The wallet checks if the account has > 0 sent / received transactions. If there are transactions on the account, the account is imported to the wallet. If there are no transactions on the account, the loop stops.
Sometimes the import also already contains the number of accounts - then the check of number of transactions is not required.
is it ever possible for two independent wallets to have the same mnemonic seed phrase?. If Yes, what's the implication? If No, why?
Theoretically possible.
Bug in implementation of generating randomness. If both wallets decide that "random number is 6", then the same "random" seed is generated on both.
Statistical probability that both generate truly random seed and the seed is the same, is very very very low. Practically impossible even if the machine was trying to generate seeds over and over for trillions of years until it finds the same seed. But statistically, the probability is non-zero.
tips on security measures to observe when providing mnemonic seed phrases for crypto wallets?
If possible, use input from the user to help generate the seed. For example some apps collect user mouse movements (presumably unique for each user / session) when generating the seed.
Encryption. Keep the raw data stored in an encrypted form, with access control - e.g. short-lived or one-time-access tokens.