"He reads several newspapers."
Translation:Hij leest verscheidene kranten.
In this sentence they can be used interchangeably. However, verschillende also has a second meaning, that verscheidene does not: it can also mean "different".
"Hij leest verschillende/verscheidene kranten" - "He reads various newspapers"
"Hij leest twee verschillende kranten" - "He reads two different newpapers"
"Hij leest twee verscheidene kranten" - Makes no sense.
Well, 'veel' means many... But, in any case, as 'kranten', being a plural, has commen gender, the adjective carries the common gender inflection. So my guess is that it should have been 'vele kranten'...
But I think there's probably a subtle difference in meaning between 'many' and 'several'. The way I see it, several means a number that is not as big as many.