Is Muhammad (PBUH) Infallible according to Shia Islam?

> Infallible - Incapable of making mistakes or being wrong My question is, How Is Muhammad PBUH infallible according to Shia Islam because * His best friends were Abu Bakr (RA) and Umar (RA), many Shia believe they will go to Hell. * His favorite wife was Aisha. He even choose to die with her. Many Shia believe Aisha (RA) was not a perfect woman and created a lot of rift esp at the time of Muhammad PBUH death. Again the prophet trusted her to die with her and she deceived him? * When the prophet saw men pollinating date treats. He asked them what are you doing. They said pollinating date tees. The prophet forbade thee from doing so, so they stopped. The next season there were no dates. The prophet realized he was wrong so he allowed them pollinate trees again. * The prophet ate morsel of food that had poison in it from Jews women. His two companion died (this would be a clear embarrassment for a prophet). The jews woman was open to accept him as prophet if he did not die. But the prophet ate it and realized there was poison so he stopped. So was he infallible? If not, what does infallible means?