How necessary were squires in helping knights get into and out of their armour? If a knight’s squire were killed or indisposed, would he still be able to get his own armour on?

Squires sped up the process, but they weren’t just there to help the knights get their armor on. In the midst of battle, squires were there to pass on a fresh mount if the knight’s horse foundered or was injured, or a spare weapon if the knight’s own was broken or lost in the chaos of battle, and of course, squires were also there to fight just like any other man-at-arms.

But yes, a knight could definitely armor themselves when necessary. It was somewhat difficult on one’s own, there was a tendency to cut corners to save time (leaving one side fastened so that you sort of step into it sideways and then only have to do up the other side), which raised the possibility that they might miss some fiddly but important step and leave a vulnerability exposed.