Consider the molecule 1-chloroethane
Let carbon attached to $\ce{Cl}$ be $\ce{C1}$ and other one be $\ce{C2}$. While learning inductive effect I was told that $\ce{Cl}$ due to high electronegativity pulls the $\ce{C1–Cl}$ bond electrons towards itself leading to development of partial positive charge on $\ce{C1}$ and partial negative charge on $\ce{Cl}$ .Now this $\ce{C1}$ which has became a little electron-deficient tries to pull electron of the adjacent adjacent carbon $\ce{C2}$ leading to development of a further smaller partial charge on $\ce{C2}$. I have following doubts:
Will $\ce{C1}$ only pull electrons from $\ce{C2}$ or from the hydrogen atom attached to it also. I think it does pull, but then why don't we take that pull into consideration?
When $\ce{C1}$ pulls electrons from $\ce{C2}$, the partial positive charge developed on it due to the pull of electrons by the chlorine atom will be reduced a little but why do we then show $\ce{C1}$ to have same partial positive charge?