Note that the questions should be about bitcoin, and therefore, so are the answers. Any other cryptocurrency MetaMask supports might not have the same procedure for generating private keys.
Also, this has nothing to do with the Bitcoin Core development.
If I download an app such as Metamask which will give me a seed phrase, how can this seed phrase be transformed into an alphanumerical private key.
The seed phrase isn't transformed into any private key; the private keys are derived in a deterministic way. With the seed phrase, which is a representation of a seed (the big number), you can have extended master private keys that are used to derive ECDSA private keys.
For more info see: HD wallets
Also, where is this private key stored - is it stored locally within the app or is it stored within the actual hardware of my device.
Depends. If you use a hardware wallet, the master private key is stored in it, and only signatures are transacted, while if you've installed a wallet software in your PC, it either stores your seed phrase or your master private key in your hard drive.
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