There seems to be some regional variation on this topic, so I will report from my AmE perspective.
In your particular example, either option would be understood to mean the same thing: the speaker works at some point during the course of each weekday (Monday, Tuesday, Wednesday, Thursday, Friday).
“From” would probably be omitted in either case as it is not needed to indicate a day range.
Generally speaking, I was always taught to indicate inclusive ranges with the word “through”. This generally has more application in studying mathematics, but could have an impact such as the following:
- Read up through chapter 3.
- Read up to chapter 3.
Receiving instruction #1 with no further clarification, I would read chapters 1, 2, and 3. Instruction #2, on the other hand, presents a quandary. It seems most likely that I’m supposed to read chapters 1 and 2, stopping when I reach the start of chapter 3, and that’s indeed what I would think if I were given no other hint as to the instructor’s wishes.
As you can see there’s a lot of iffiness here, so even among native speakers there is occasionally confusion and/or clarification. A misunderstanding such as the following would not be unheard of:
A: We’ll be on the boat Wednesday to Saturday next week.
B: So you’ll be back on land that Saturday?
A: No, we dock Sunday morning and we’re spending Sunday on the road.
As always, consider your audience and the context. Working those five days is such a common occurrence that neither word is likely to confuse anyone as to what you mean. In other cases, you may wish to add “inclusive” after the range to clarify that the whole of the end-limit you’ve named should be considered part of the deal.
The word via is used for through, which can also be an abbreviated form of through the medium of.
So "talking via Skype" is used to indicate that the conversation was done through the medium of Skype.
I can use the words by and via when talking about a place. For example:
I travelled to Wales going via Birmingham.
I travelled to Wales going by Birmingham.
These now have two different meanings. Going via Birmingham still means to go through Birmingham. The route goes right into Birmingham and out again. Conversely, when going by Birmingham it just indicates the route came adjacent to the city and does not enter it.
So they can be used in similar circumstances, but have similar but different meanings.
Best Answer
The addition of up or down in these types of phrases can be either literal or figurative, depending on context.
By literal, I mean that the person is literally ascending or descending in space. Usually this means ascending or descending a hill, ladder, staircase, elevator, etc. For example, if I'm on the 3rd floor of a building and Frank is on the 2nd, I might text him saying, "Come up to the meeting room, we're waiting for you."
There are several figurative uses of "go up/down":
In context
Since you mentioned that you draw your examples from Oscar Wilde's well known play The Importance of Being Earnest, I'll examine those examples in that context.
...
Possibly, Dr. Chasuble is literally coming up, in the sense of ascending a hill. In context, Cecily is probably closer to the house than Dr. Chasuble, and Wilde could have written it this way to say he is coming "up" toward the house.
In the previous act, Jack was in London, where he remains at the time of this scene. Cecily refers to him having gone to London as having gone up to the city from their country house in the British style I mentioned earlier.