I checked the website and all Eiffel Tower tickets are sold out for the week that I am interested in. Can you buy tickets in advance in person?
No, just get in the ticket line whenever you decide to go.
As Tim said.. no.. advance tickets are available only online. But.. its not such a big deal.. first off you can always just wait in line. its what most folks do.. or you could wait in a much shorter line if you elect to take the stairs.. ( and its cheaper) or you could go online and check if tickets for your dates are available to the SECOND level.. and from there simply get in the much shorter line on the second level for tickets to the top.. or not go to the top( I think its overated.. view is awesome from second level) or you could check online if they have tickets for a the tour called "Eiffel Tour Behind the Scenes" .. costs a bit more then a regular ticket but gets you to the second level and with no wait( and apparently the tour is very interesting).. So lots of options.
You might consider Paris Vision tours. We used them for several tours, one of which was the Eiffel Tower, packaged with a river cruise and a bus tour of some Paris sights. I don't remember it being particulary too expensive and it was worth avoiding the hastle and waste of time waiting to get tickets for the Eiffel Tower.