The best solution depends very much on what you are measuring, and how you are measuring it, so it's difficult to give a useful answer to your question. There is no such thing as a "most correct estimate" or "most accurate value."
(1) The *most popular* theory is to assume that I is independent with V when you are in ion saturation. Is that not the case in you I-V curve? If not, then you could be dealing with sheath expansion, or your probe could be perturbing the plasma.
(2) I believe this is very typical. I have not seen very many examples where the plasma potential could be determined precisely using the transition to the electron saturation region. You can estimate the local plasma potential using the sheath relation if you know the composition of the plasma.
If it's still useful to you, here's some old code I had used a long time ago. Not sure which version was my "final" one, or what was the format of the data that was supposed to be loaded.
Hope it helps. Be aware it is not the "most correct estimate" as Cedric points out, since all experiments will deviate from the very simple ideal theory, and if I recall correctly my code pretty explicitly asks the user to choose some points "by eye". Here are some other references
It looks ok to me for a simple estimate, which is often all that is required. There are often very subtle issues if you need a very accurate answer. It looks like when calculating density you are assuming Te=1eV which is probably reasonable but may not be self-consistent with your Te measurement.
I am calculation ne from Ion saturation by fitting a line from 2 points then I calculate the Te from slope of line fitted in the exponential region of the Electron current region.
Yes but it doesn't look like you are using your fit for Te in the calculation of the ion sound speed to convert Isat to be, it looks like you are using Te=11000K=1eV