I have two DB tables, ACTIVITY and USER.
In the ACTIVITY table I have 3 fields AssignedTo, CreatedBy and LastModifiedBy that need to be related (1 to many, so that a user can create, modify and be assigned to many activities) with UserId field and primary key of the USER table.
Is it a good practice to create three different relationships between the two tables, all three connected with the primary key, in this case UserId, of the parent table?
Yes, nothing wrong with that. Just do it, it is correct.
While thinking about it: You might take a look at versioning of records. That is a step further but gives you even more info about who edited a record and when.