No, but you could say "top cop" to mean high-ranking or senior. You might find this in a newspaper headline where short words are often preferred, to save space and appear more eye-catching to the reader.

Generally no. There are only a few limited situations where 'big' could mean 'important', instead of 'fat', and the only example I can think of is 'big boss'. 'Big cop' would always mean physically large to me. Not necessarily fat - possibly very tall and solid. But still physically large. And similarly with 'small' - that would almost always mean physically small. Why do you particularly want to use 'big', given that it is not an appropriate word in that context?

As per the other responders, you would not use big or small here. Maybe senior or junior. In this case it would not express age as it might normally do, but would be appropriate for high ranking and low ranking. (The fact that this is often coincident with old or young age is merely a fact of real life, not grammar!)

Big boss is a common phrase for the man at the very top of the chain of command. That's the only time or way it is ever used. Only use the terms big boss or top dog informally. amongst your friends and workmates, to mean the man at the very top. For describing rank it is high ranking or low ranking, medium ranking is a little less common. (In the UK). We would use their actual position. Foreman, supervisor etc. For people in the middle of the chain.

I can't think of any substitute for high-ranking or any synonyms that will mean the same also with low ranking because you are referring to their rank it can only be high, low or medium. High level, low level or medium level cop are all I can think of.