Learn Dutch: Hierdoor verlamt de elektriciteit de hele wijk. - As a result the electricity paralyses the whole district.

Because the sentence starts with the causal adverb hierdoor (as a result / because of this). In Dutch main clauses, the finite verb must always sit in the second position (the V2 rule). Since hierdoor takes up the first position, the subject is forced to move right after the verb, which is called inversion.

Could I use daardoor instead of hierdoor in this sentence?

Yes, they are usually interchangeable in this context. Hierdoor literally means 'through this' (because of this), while daardoor means 'through that' (because of that). Hierdoor feels slightly more immediate or closer to the speaker, but both are causal demonstrative adverbs that trigger the exact same V2 inversion.

Why does heel get an extra -e in de hele wijk?

Wijk (district or neighborhood) is a de-word. When you place an adjective before a noun that is preceded by de, the adjective gets an -e ending. Notice how the spelling changes from heel to hele with a single e: this keeps the vowel sound long while following Dutch open-syllable spelling rules.

Is it normal to use verlammen (to paralyze) for inanimate things like a district?

Yes! While verlammen is used medically for physical paralysis, it is very commonly used metaphorically in Dutch to describe bringing infrastructure, traffic, or society to a complete standstill, just like in English.