step down/ undermining German society/ undermine confidence/ undermining the cliffs

[vil]

Dear teachers,
Would you tell me whether I am right with my interpretation of the expressions in bold in the following sentences?
Thilo Sarrazin, a member of Germany's central bank, has stepped down. He now presents a problem for his political party, the Social Democrats, after claiming in a new book that Muslims are undermining German society.


step down = resign from office

undermine = destroy property or hinder normal operations; destabilize

Nationalization would undermine confidence in the financial system.

undermine confidence = to cause distrust

The sea is undermining the cliffs.

undermine = wash away

Thank you for your efforts.


Regards,


V

[Tdol]

Undermine here seems to me to be like weaken.