Constants and variables of a certain type can't be declared again with the same name, nor can they be altered to store different types.
After 'nor' why 'can' is used first instead of 'they'? I feel like it should be 'nor they can be...'
It's true that in most English clauses, the subject comes before the verb. Then again, inversion is quite common. The two main types of inversion in English are subject-verb inversion (Into the room will come a unicorn--an example on the Wikipedia page), and subject-auxiliary inversion (also known as SAI). Your example sentence is an example of SAI.
Subject-auxiliary inversion (SAI) should not be new to you, because it happens in questions (e.g., Will you help him?), but SAI also happens after negative (never, not, nor) or restrictive (think only, hardly, seldom, and such) expressions. For example:
Never have we been more close.
Not until he had finished his coffee did he consider food.
Only after two billion years did the first cell emerge.
Seldom have I heard such nonsense.
In your example, nor triggers the subject-auxiliary inversion. That's why it is ..., nor can they be altered to store different types.
For more information, see our questions tagged subj-aux-inversion.