I have some question to ask, what actually is checksum in mnemonic seed phrases, what's the difference between seed phrase with valid checksum and the one with invalid checksum in respect to wallet vulnerability to be easily attack/brute force.
Each word in a seed phrase encodes 11 bits of data. A 12 word seed phrase has 128 bits of entropy. The checksum is calculated using hash functions and then appended to the end of the 128 bits to give 132 bits in total, which then encodes in to 12 words. (12 words x 11 bits = 132 bits). The last word of the seed phrase, then, includes some entropy and the checksum. For a 24 word phrase, it is 256 bits of entropy and 8 bits of checksum. In terms of how this looks, a seed phrase with the incorrect checksum will have a different last word.
In terms of being attacked by brute force, most attackers are presumably only going to try seed phrases with correct checksums since no wallet will generate a seed phrase with an incorrect checksum.
I'm getting to understand something here, manually selecting randomness of seed and seed extension( I mean adding additional word making the 13th word) is the same thing?
There is no such thing as manually selecting randomness. Humans cannot be truly random. Any source of entropy needs to come from something like coin flips or the /dev/urandom function.