From The Pavilion

Is there a way we can find records like Most Career Runs/Wickets, Highest Runs in an Innings, Best Bowling Figures, Most Matches Played, Most Catches Taken, etc?

Yes you want - Club > stats centre > club records

What Carrot suggested will show them for your club. I do not believe there is a public register of those stats all time by any player/club in the history of the game.