"By Monday" technically means "before Monday" – that is, on or before 23:59:59.9(9) on Sunday night. However, the actual definition can be less strict. In the context of business, it may be delivered on Monday before business hours (most likely before 09:00, although it can earlier or later in some places).
There is no real difference between sentences #1 and #2 in your question, although I would expect that sentence #2:
I have sent you a dictionary, you will receive it by Monday.
Will be heard more often than sentence #1.
The sentences you have used should use a period or include a conjunction:
I have sent you a dictionary. You will receive it by Monday.
I have sent you a dictionary, and you will receive it by Monday.
The answer by Cookie Monster includes a common way of saying this, but it is different. "You will get it this Monday" means "it will arrive on Monday" and does not mean that it may arrive before Monday, or that it will arrive before Monday. A way of phrasing your sentence in a manner similar to that used by Cookie Monster, while retaining the same meaning, would be:
I have sent you a dictionary. You will get it by Monday.
You could also say:
I have sent you a dictionary. ...
It will arrive by Monday.
It will have arrived by Monday.
You will have it by Monday.
You will have got it by Monday.
It will be delivered by Monday.
It will have been delivered by Monday.
You may also be interested in this resource for the difference between the tenses: