Zyada has taken belly dancing leasons. Hopefully she can drop in and provide some information.
Fencing while belly dancing is properly called sword dancing (and is sometimes a staple of male belly dancers’ routines). It’s very fun to watch.
I’ve done/do belly dancing (mix of styles), and the thing I hear the most of people who are new to it is “I didn’t realize how much of a workout I was getting!” Aerobic, strength, endurance, flexibility: all of these are involved. (Try holding your arms up and moving them about for the duration of a typical song, now imagine doing this for a typical full-length routine! Depending on the style, you may not get much of a chance to put your arms down and rest.)
As to if an 8-week class is enough, it really depends on how their classes are set up. Some places I’ve been 8 weeks is enough for the next level, others recommend you take at least 2 beginner’s courses before continuing on. As an example, one place I went had about three or four beginner’s dances, and in each 8-week session you learned one dance. Each dance covered the basic moves, just strung together differently. They also would do what I’d call ‘free for all dancing’ to let you get used to improvising and not feel like all you could do were set pieces. The next level of courses were setup the same, introducing more advanced movements. The top level courses were meant more for those who wanted to join the dance troupe.
As for belly dance costumes: unless you’re performing, all you really need is something you feel comfortable moving about in and a hip scarf of some sort so you can better see what your hips are doing. But it is easy to be enticed into buying lots of pretty shiny things (or beautiful tribal items which tend to be not sparkley): take a peek here for some ideas.
Just remember in belly dancing, no duck butt! 
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Yup. Keep your butt tucked in, lengthen your back, and don’t hunch forward.
I’ve found that hip scarves ten to last for about a year of practice before they shed beads and coins everywhere. Iwouldn’t spend a huge amount on one.