Not always 'but'. Sometimes it just links the sentences together kinda like an 'and'. The nuance is more like tomorrow is saturday... and aren't you going to go somewhere?
Note that many japanese like to use desuga to replace "wa" in speaking so to soften their tone a bit. I'd say don't worry too much about it.
Right. It's somewhat confusing.
For some reason, a formal-looking document often uses this sort of "ga",
which is sometimes misleading for Japanese people too.