What happens to the amino acid when it is in a solution with the pH of its isoelectric point? (zwitterions)
The accepted definition by IUPAC gold book is: The pH value at which the net electric charge of an elementary entity is zero. pI is a commonly used symbol for this kind-of-quantity. It should be replaced by pH(I) because it is a pH determined under that particular condition.

The solubility of an amino acid is the smallest at its isoelectric point and it easily precipitates.

For question 4 you need to be familiar with dynamic equilibirum. The zwitterion accepts and loses protons all the time, but at the isoelectric point, its concentration is the biggest among all the forms of the amino acid, that is, the species that has a protonated carboxylic group, would easier lose that proton than the zwitterion's carboxylic group would accept a proton.