is it cheaper to buy a ticket at the Alamodome then online ?

Most definitely cheaper in person at the box office. You don't pay all the extra fees.

I went to the Dome for a graduation, so I didn't have to buy one. Although I was told its cheaper online.

Depends on the event, but more times than not, it is usually cheaper on line

No

Yes

Depends what event some events release tickets before show and there is no service charge

Usually cheaper online