This electric hot water heater was installed four or five years ago.

My first question is about the rust-colored corrosion shown below:
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Should I use a paste made out of baking soda or something and (try to) scrub this stuff off, or should I contact the landlord, or... ?

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What would be the best way/materials to keep creepy crawlies (spiders) from entering through these messes left in the wall?

Any help would be greatly appreciated!