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until versus at and by

2 years ago
In Q8 the key says at/by. I have chose until.

1) Tell me please is my answer correct? If it is not correct could you explain why? 2) Do I understand correctly that in "I’ll be in Sydney (8) ___?__ the end of next week" it means "I’ll be staying in Sydney (8) ___?__ the end of next week". 3) Would the answer be different if the meaning was I'll reach Sydney only closer to the end of next week?
Just a quick message (1) before I leave for the airport. Sorry I haven’t been in touch (2) since Wednesday, but I’ve been busy getting ready (3) all week and I haven’t collected my ticket (4) yet from the travel agency. (5) As soon as I get to Sydney, I’ll send you an e-mail. I’ve (6) never been to Australia before but I’ve been reading a lot about it (7) lately / recently. It sounds great! I’ll be in Sydney (8) ___?__ the end of next week, and then I’m travelling to Melbourne. I’ll be there (9) _?___ a month.
Thank you!