1- No, just no. Knighthood does not get handed out like sports trophies. Knighthood is a title of nobility, and nobility is typically either a thing granted by birthright, or a thing granted by exceedingly outstanding military service over the course of years or even decades. Sure, in the modern world nobility means so little that the Queen can grant the title to whomever she pleases, even random musicians, but that's the modern world.
But back in the day? Any medieval era ruler offers up the opportunity to win a noble title... and they face rebellion from their own current nobles who will feel both insulted and threatened. Commoners were considered inferior creatures... closer to animal than human. I want you to imagine a US president appointing a squirrel to the position of Supreme Court Justice. That's the level of absurdity in appointing a commoner as a knight.
2. Unlikely. A sword going through bone that thick at that sort of angle in tournament armor is just not very likely at all. What would make sense is a foot wound that gets infected. More soldiers back in ye olden days died of gangrene than died in combat.
In fact, some medieval soldiers took to dipping their weapons in animal or human offal, knowing that their soiled weapons would have a greater chance of causing a deadly infection and killing the enemy even if they survived the combat.
3. We've already shot the knight thing in the proverbial foot. It will never happen. Standing or otherwise.
4. That is not how peg legs work. In the Real World, amputated limbs were often cauterized- not by metal, but using hot coals. But more often allowed to heal naturally rather than with burning. Then the artificial limb (aka- peg leg) is put on using leather straps so that it can be removed. And you do need to be able to remove it, so that you can clean the stump and repair the prosthetic.
*Grafting* the peg leg onto the body... guarantees death by infection.
5. Recovering from an amputation enough to fight in just three days? Well... humans are *damn* tough animals, and there are many examples of extraordinary real world men who overcame far worse hardships. Like being mauled by a grizzly bear, then making a thousand mile trek on foot through wilderness to reach civilization. So that part is believable. It's everything else that's not.
How I'd fix this setup to make it believable:
1- Drop the tournament stuff. Most people roll their eyes at tournament arcs, anyway. Instead, make it *an actual, real war*. Depending on era, it may be a very small scale war... during the bronze age, it was rare to see an army with more than a hundred soldiers in it. Pillaging and/or being granted minor titles was a common means of paying soldiers in the ancient world. Especially pillaging... everyone loves a good pillage...
Or, make him on the side trying to stop a pillage. That's just as viable.
2- Swap out getting foot cut off by enemy, and have it be an infected wound that forces the doctor to amputate. It was very common back then (and 'back then' includes 'just about any point of history up to and including World War 2'), so having it happen to your character is to be expected. It *also* gives you a great opportunity to describe the doctor spending several minutes sawing through his lower shin. Without pain killers.
3- He just lost a foot, it's reasonable that he'd be told he can't be part of the army since he can no longer march with other soldiers.
4- Scavenging materials and cobbling together a peg is reasonable. It's not a complex science, really only requires some straps of leather, part of a bench, and a good knife.
5- It'd be more interesting if the army left him behind and he manages to catch up to them later.
That's what I'd do to keep things respectable with those of us who respect realism in our storytelling.