A spectrum , simply defined here , is a band or range of colours like the rainbow . 'On the opposite end of the spectrum' is a metaphor which means that of are many possibllities like the range of colours in a rainbow ,and the one you are refering to is on the other end- the opposite . eg We have friendly customers in our place , but sometimes we have customers that are from on the opposite end of the spectrum who are very rude. On the opposite end of the spectrum , we have students who drive flashy cars to school , unlike the many who drive the conventional .

Not really. On the opposite end of the spectum implies that the two things you are comparing are as far apart as they can possibly be - there couldn't be two things that are more different from each other. On the other hand merely expresses an alternative - it could be very different from the first option, or only slightly different. OTOH is used to weigh up two choices and decide which is better.

On the other hand of the spectrum, is a way of saying, the complete opposite. Like white is on the other side of the spectrum of black or fire is on the other end of the spectrum of ice. You use "on the other hand" when you're talking about options. Such as: "I might go to the store right now, but on the other hand, I might go later when its less busy." or, "The BMW is a very luxurious car, but on the other hand, the Volvo is much safe"