"How does a law suit get that far if there is no basis for the case? Is it simply an issue of the Plaintif getting her day(s) in court?"

Not knowing what happened before trial I can only make an educated guess. The defense usually moves for summary judgment before trial submitting affidavits showing that the plaintiff cannot (in lay terms) make her case. Judges are reluctant to grant these motions unless it is clear from the pre-trial evidence that the plaintiff cannot prevail. If so and the trial comes on when the plaintiff rests and the defense makes its usual motion to dismiss the judge asks the question, "looking at all of plaintiff's evidence can reasonable jurors disagree?" If she feels they can then she denies the motion--otherwise, out goes the case. Why wait and not dimiss before hand? 1) she may have said she had evidence but not produced it; or 2) the judge may have given her, a lay person, a great deal of latitude.

From your description of the exhibits you saw but apparently weren't put into evidence there may be many reasons for this. Pltff may not have realized she had to offer them (after authenticating them); or she may have already been told by the judge that they were inadmissible--though why the jurors would see them is beyond me.

Wouldn't the Court have reviewed all of the potential exhibits and the deposition before a jury was seated? In a civil action, probably yes, but the plaintiff being a lay person may not have handled the pre-trial prcoceedings properly.

Who pays the cost of the two days of proceedings? Taxpayers? Plaintif? Most courts have rules assessing costs and even fines for frivolous law suits. But costs can be awarded to the victorious party; that would be determined away from the jury; and costs are only a fraction of the true cost of the law suit.
Why, generally, does one choose not to seek representation? Is it usually a matter of $$$$? Ego?? Delusions?? Who knows? People are complex and you'd need much more information to answer that question.
In light of my stating that I had been accused of discrimination based on National Origin, do you think I was chosen as a juror in this case by the Plaintif or the Defense? The attorneys don't "choose" who to be seated; instead they have limited number of peremptory challenges to use to get rid of people they don't want. My guess is that the Df would want you on and the Pltff didn't know any better or didn't think through what it meant to be sued. Or she could used her peremptory challenges and was stuck with you.

I guess the moral of the story is that as much abuse as Lawyers receive, they are sometimes (IMO)essential [grin] [Always, Murphy, alwwys.
BTW, I have gotten the desire to serve on a jury out of my system and hope to never be called on to do it again. {unfortunately, in New York, at least once called you are likely to be recalled in the future.].

Find the Ghost