Yes, indeed, you may say look down upon (or on); divinities, kings, employers and such superior beings are often spoken of as looking down upon their worshippers, subjects and employees—sometimes benevolently, sometimes wrathfully—and someone on a high building or mountain may look down upon the street or valley below.
Down and upon are not opposite but supplementary here. Down, which is employed as an adverb, not a preposition, designates the direction of looking: the subject is above what is being looked at. Upon is a preposition and heads a prepositional phrase designating what or who is looked at.
There is also a figurative use of the same idea to mean regard with scorn; the subject treats what is looked at as if it were “lower”—inferior:
Students from affluent families look down on those whose families cannot provide them fashionable clothing.
Many 18th- and early 19th-century grammarians looked down upon the recently invented passive progressive construction.
On is more often used with the figurative use and upon with the literal use; but this is by no means a rule.
The collocation VERB + ADVERB of direction + Prepositional phrase is perfectly ordinary: look up at/to, poke around in, put up with, get away with. In many cases a collocation has an idiomatic sense which cannot be derived by analysis of its components, and such collocations are often classed as phrasal verbs; but this is not the case with look down upon.
"Walk through the tunnel" means to enter the tunnel on one end and emerge out the other end.
"Walk across the tunnel" could mean the same thing, but only if the context establishes that. It could also mean to enter the tunnel through a side entrance, and exit out another side entrance (i.e. the short way, not the long way); or it could mean to go across the top of the tunnel (e.g. if it's underground and the road goes over it); or variations on those themes.
In general, "through" implies entering the middle of something and then going out the other side, whereas "across" implies crossing the middle, but not necessarily going in the thing you're crossing.
Best Answer
If the walk is a destination/event (such as a walk to end cancer, a school walk-a-thon, etc.), you could use "go to a walk" or "go to the walk."
However, in most circumstances, "walk" does not represent a destination/event, and you should say "go for a walk."
This web page might help you out further (Collins Dictionary) by giving you some example sentences.