1. Why is Fay Stationary? She is in the same exact place she was when I left at around 6:30pm EST. Is there a meteorological reason she is not going anywhere?

Fay is not *really* stationary. She is moving to the NNE at around 3-4 mph, over all. The reason tropical cyclones may slow down or stall is almost always because steering currents become light, conflicting, or virtually non-existent, for a spell. Fay may be heading a touch east of NNE, now.

2. There has been some talk about Fay coming back toward us. What does this mean? Why would a Tropical Storm come back the way it entered? In this case, would she be much severe?

Fay is not likely to come back exactly the way she entered.
The reason for the course correction has to do with steering currents, which are now going to be blowing from the east-northeast ,east, and east-southeast, instead of out of the south, and southwest.
She may or may not be any more intense. A lot of this depends on whether or not she spends any time back out over water.

3. What are the chances of fay sticking around and the other Invest catching up to her? I know this sounds stupid on my part and all, but what is the likelihood of this happening?

In most cases, the odds would be very low. In this particular case, it is in the realm of possibilities.

4. Why are all of the weather plots just throwing Fay all over the place? Where does the NHC, UKMET and other data plotters or what ever you call them get their data from? How do they predict where the storm will be? Why are they changing so sporadically?

The NHC is not a model. NHC stands for National Hurricane Center, which is the public tropical foresting arm of the National Weather Service.

The NHC creates their own plots, using a blend of models weighted for accuracy and human forecaster experience.

UKMET is a model. UKMET stands for United Kingdom Meteorological, from where the run comes.

For the most part, with models, computers dissect the data that is fed into them, and using a certain degree of AI, are able to create tracks and intensities of tropical cyclones within a range of probabilities that sometimes make them useful.

Lastly, what is Fay's overall plans? Things look like she is trying to strengthen but is having trouble doing so. She is defiantly one of my weirdest storms I've ever tracked, and quite interesting for my first storm. I have another thought on my mind. Why is is still Windy in Fort Myers? Were getting the same tropical conditions we have been getting all day. Wind Gusts are the same as they were when Fay was here. The rain has stopped since the sun went down. Any probable reasons for all of this?

Fay doesn't have "plans," as much as "plans" will be made *for* Fay.

She is a very weird storm, indeed. Pretty fascinating. I'm sure many a thesis will be conjured up after this week.

Fay's windfield is pretty broad, and she did not weaken at all most of the day.

As for the rain stopping since the sun went down, I doubt that there is any significant connection. More probably, this is because you are now on the subsident side of the cyclone, with drier winds coming in out of the northwest, while at the same time Fay herself has passed well to your east.