I have an above average knowledge about Bitcoin network
I've been actively involved with Bitcoin technology for 6 years, and often educate others on the details of transactions that I'm familiar with, and yet I still wouldn't say that I have an "above average knowledge about Bitcoin network". I suggest you assume that you know very little and focus on learning more.
but I lack some advanced understanding as how transaction works. So I hope you can clear this that is in my mind for some time.
I'll give it a try.
I know that it is possible to purge a transaction nullifying it, for example if you sent a transaction with a low fee it will remain unconfirmed for some time and it gives you the opportunity to purge it so it will be canceled and your balance will be fully restored in your wallet.
This is not true. There is no way to force peers in the peer-to-peer network to do anything. If they don't want to purge your transaction from their memory, they don't have to, and they won't.
My doubt resides on it, considering that my previous statement is true (please correct it if it's not),
It is not.
is it possible to set a server with automated bots that will be checking the mempool/network for unauthorized transactions comming from your wallet and auto purge them to prevent it?
There is no such thing as "the mempool". Every node maintains their own mempool. Every node decides for themselves (or runs software that decides for them) which transactions to store in their own mempool, and when to remove those transactions from their own mempool. There is not protocol for telling any node to remove anything from their mempool.
If what I said is not possible by any reason,
It is not.
please explain
There is no command that you can give to a node to tell it to remove a transaction from its mempool. If a node does remove a transaction from its own mempool, it does not tell any peers that it has done so.
and if you have the knowledge, please try to answer this as well: is there any coin that allows it?
This is the Bitcoin forum. I have no knowledge about altcoins. You should ask altcoin questions in the altcoin-subforum. Any attempt to discuss altcoins in this sub-forum will be reported to a moderator so that this thread can be locked.