imperative sentences - Use of be+infinitive in different meanings

I know that be + infinitive is used for order, instruction and plan but some of the example sentences are confusing to me they are:

1. 
   

   I'm to go now. ( what's the meaning of this sentence ?)

   
   


2. 
   

   Mr johns was to speak at the meeting last monday. ( if this sentence is about past plan, was the plan fulfilled ? Or what's the meanings of this sentence ?)

   
   


3. 
   

   You are to be on time.(what kind of meaning this sentence implies?)

   
   
   


4. 
   

   Am I to believe what they say ? ( what kind of meaning this sentence conveys ?) Now, if the meaning of those sentences is similar to 'supposed to', why be+infini' is used instead of supposed to' ? Is 'supposed to' is the same as 'should' or what? I'm expecting understandable answer. Thank you in advance.