About the zombie rule, Is it strange When in the resident evil games the player gets bitten or attacked by virulent monsters, only by simply losing health rather showing signs of infection(except resident evil:outbreak and its sequel)like they were never infected, while many minor and supporting characters ended up been bitten, attacked, transform into monsters and eventually end up dead?

Not at all, it's been accepted that canonically the player never gets infected since it is possible to beat the games without getting hit/bitten. In reality it's very possible they didn't have room or technology to add a working infection system in the games until the Outbreak series, or simply didn't feel like it.

It is stated in the first game that 1 in some number of people are immune to the T-virus, and it is believed that the main characters are among these people who are immune.

Jill certainly WASN'T, though. At least not the super version carried by Nemesis. They made a huge deal about needing the T Vaccine in 3 and then made it a plot point in 5.