you can live without ur appendix. it has no real crucial function in maintaining your body health. maybe the machine required an organ or something of sydney's. and because you really don't need ur appendix. they took that. just a guess.
Why would they show the scar on her stomach? they don't just show somethign on this show that has no meaning. is it to merely reitorraite that shes has no idea whats has happned to her and that she has been gone for a while? or maybe its meaning will be more cruicial.