How does the tx fee in sendmany method get calculated? In sendmany there is a conf_target parameter with the comment "Confirmation target (in blocks)". Does that mean that Bitcoin Core implicitly calculates and sets a smart fee for a given block target?

If so what is the priorities if I:  


Set TX fee explicitly before  
Set conf_target == 1  
Set estimate_mode == UNSET  


What will be the resulting fee rate on the transaction in each case?
Does that mean that Bitcoin Core implicitly calculates and sets a smart fee for a given block target?


Yes that's how fee estimation work (basically statistics are made out of the transactions you relay given their feerate and how many blocks it takes for them to be confirmed).


  If so what is the priorities if I:
  
  
  Set TX fee explicitly before
  Set conf_target == 1
  Set estimate_mode == UNSET
  


Assuming you mean calling settxfee by "Set TX fee explicitly before".

The command parameters take precedence over globally-defined parameter, so the conf_target parameter will be used for fee calculation.

Setting estimate_mode to UNSET will make the decision of using conservative estimates depending on either you signal for RBF (use ECONOMICAL) or not (use CONSERVATIVE).