The differences between the two modals ‘will’ and ‘shall’ are many but basically ‘shall’ is the stronger and more forceful. ‘Will’ is usually associated with ‘intending’ ‘wishing’ ‘wanting’ and so on and ‘shall’ has a sense of determination and also compulsion. When you say: I shall pass that examination even if it’s the last thing I do, you are really saying that nothing is going to stop you. ‘Shall’ is often used in the first person ‘I’ and ‘we’. When therefore we use ‘shall’ with second and third person ‘you’ ‘he’ ‘they’, we are telling this second or third person exactly what they must do and we are in a sense forcing them to do something. In your sentence ‘shall complete’ you are telling the contractor what must be done.
“alternative” describes a different option that is available, or a different choice that can be made. For example, “The road is closed, so we must look for an alternative route.”
“alternate” describes a switching back and forth between two things in sequence. For example, “Even numbers alternate with odd numbers” (one is an odd number, then two is an even number, then three is an odd number, and so on).
As an adjective, “alternate” seems to be increasingly used to mean the same as “alternative”. In British English this is viewed as an error. I believe it may be more accepted in American English.
However, I think I am not clear about ‘‘As an adjective, “alternate” seems to be increasingly used to mean the same as “alternative”. In British English this is viewed as an error. I believe it may be more accepted in American English.’’
Can you please provide some more details/examples based on British English?