electromagnetism - Transformers: relation between their current, voltage and resistance

My current understanding

Transformers are used to step up and down voltage keeping power constant. Hence, for example, if I step up some voltage, the current will decrease in the secondary circuit.

The issue I have

I am not able to digest the fact that on applying more voltage across a circuit, current decreases. To me it seems that the extra potential difference should make the electrons zoom faster.

My guess

It occurred to me that maybe, for example during step up, due to the fact that there are more coils in the secondary circuit, the resistance of the secondary circuit increases and this increase in resistance reduces the current, although there is a higher voltage.

But then I thought that if we use another material in the secondary coil, that has lesser resistivity, such that even on making more number of turns, it has a resistance equal to that if the primary coil, then what happens?

The analogy I want to use

10 joules of energy can apply 10N for 1m or 5N got 2m. But it does the same amount of work because the first object is obviously heavier.

I would really appreciate it if someone could:

1. 
   

   Clarify how there is increase in voltage but decrease in current in secondary coil.

   
   


2. 
   

   Explain why my guess is correct or wrong

   
   



3. 
   

   Relate my analogy to the problem.

   
   


4. 
   

   Correct anything wrong in my understanding.

   
   

Thank you

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Edit:

There is one more similar question on the site, but it has a mathy answer. I'm looking for something more intuitive. (However, please include the relevant formulas.)