"The one that is above the old newspapers is nice."
Translation:Az szép, ami a régi újságok fölött van.
No, van needs to be included when you're saying something is in a location. Van is omitted only when a noun or adjective phrase is used as the predicate.
Az szép, ami lila. but Az szép, ami hátul van. (I would typically translate those as, "That which is purple is beautiful" and "The one in the back is beautiful.")
Az szép, ami arany. but Az szép, ami az asztalon van. ("That which is gold is beautiful" or "The one that is gold is beautiful", but "The one that is on the table is beautiful.")
There are two words az.
The definite article az meaning "the" loses its z when it comes before a consonant.
This is the demonstrative az meaning "that" or "that one." It does not (usually) lose its z - I think, from a Hungarian point of view it is just not as tightly bound to the immediately following word as the definite article is.
(To go a bit beyond: The demonstrative az does lose its z when it is followed by a postposition that begins with a consonant. In that case it is inseparably bound to the postposition just like an adjective or a definite article is bound to its noun, and it is as if they become one word with the z lost for phonetic ease.)