Also can I edit the seed phrase wordlists to add my own words to it in any types of BTC wallet?
No. The BIP 39 word list is standardized. The Electrum word list is hard coded. They cannot be modified.
Is there any way of generating seed phrases on my own?
You can implement your own software or find other software that is capable of generating seeds.
How does that work?
A large random number is generated and subsequently encoded into the seed phrase. For BIP 39, that process is specified in the BIP.
I never had the choice to select the 12/24 words.
You do not, and you should not, because choosing your own words is unsafe. The whole of cryptography works by choosing large random numbers such that guessing or brute forcing your specific number is basically impossible. The seed phrase is simply an extension of that, as the initial step is choosing a large random number. Skipping that step is reduction in the security of your private keys as the number is no longer random. No longer being random increases the likelihood of someone else guessing your number and therefore your private keys.