Only you can know for sure if she's pulling your leg or not, but illness is one of the generally accepted etiquette allowances for backing out of a commitment. Given the history, you might be better served not to invite her to stuff or prepare anything specially, but if I was another guest at this get-together I'd prefer she stay home if she's got a contagious disease.
As to knowing if she was getting over the flu, she might have thought until this morning that she'd be well enough to attend, and it's taking longer than she thought to shake it off. The polite action is to give her the benefit of the doubt, although again, if you have your suspicions then consider today the next time you're building a guest list.
I agree with this. If it was a one-time thing, I wouldn't blame someone for telling me they were out sick on the morning of the event, because illness can be unpredictable and I would definitely rather someone who might be contagious not
show up, than show up and infect everyone else. It would be a little irritating if I'd made special food/plans for them, but I would just think, that's life, and move on.
However, her pattern of behavior makes things more suspect. I think I would stop inviting her to small gatherings where her absence would affect things. If you're hosting an event with food that you invite her to, I do think you ought to make an effort to accommodate her dietary restrictions, though. Others on this board are really good at suggesting foods that can accommodate dietary restrictions while also being perfectly suitable for a large crowd, so you don't have to feel like the special dish you made will now go to waste.