Does the German language have any other words in which the German letter "a" corresponds to the English letter "i", e.g. Nacht/night, Macht/might?
Yes, there are lots of examples of this. In linguistics it is called "i-mutation", a feature that separates Old, Middle and New English from other Germanic and Indo-European languages. Basically it means that in certain contexts Germanic "a" is replaced by English "i".
No, it doesnt. You might find words that differ "u" to "i", "e" to "i" or "o" to "i", and also "a" to "i". The point is - Western European languages like to see vowels in strategic places for well-formed words, and the amount of vowels is simply limited.