Mandarin equivalent of 同 when the meaning is "for, on behalf of"
1) Would 和, 跟, or 给 be the right Mandarin substitute in this case?



给 in Mandarin can replace 同 in Cantonese when 同 (for me) denotes it is an order or demand


"你(同)我企喺度!"  = "你(給)我站著！" = "stand there (for me)!" (an order)

"你(同)我企喺度" = "你(和)我站著" means "you (and) I stand there" 

"你(同)我企喺度"= "你(跟)我站著" means "you (with) I stand there"


'跟/ 替' in Mandarin can replace '同' in Cantonese when '同'  means 'to, for or on behalf of'


Example: 

Mandarin: "你跟我解釋一下" = "explain it to me!" 

Mandarin: "你替我解釋一下" = "explain it for me!" 

Cantonese: "你同我解釋一下" = "explain it to/for me!"


  2) What's the right substitute for 你同我畀錢! ("You pay for me!")


See examples above:

你同我畀錢 ("you pay for me") = "你替我付錢"


  If you meant "you pay!"(an order)  then you should use '給' and wrote  "你给我付錢!"