Ground circuit and kirchhoff law(holiday 27.30)

Homework Statement

I attatched my question as a picture

The Attempt at a Solution

1.i found a solution using kirchhoff law, V1=-11V,V2=-9V
and it was correct. but im not sure that my method was right.
i know that kirchhoff law is originated from charge and energy conservation but in the problem there is a circuit which is grounded, so i think that charge can in and out through it. consequently, charge doesnt have to conserve in circuit.
can i use kirchhoff law in this problem? and why?

2.i found that current go to ground is 0 using kirchhoff law. but i don`t know why it is

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