So you have the mounted knights that may have been the equivalent of tanks, but I've heard that there where instances where unmounted knights where used in battle throught the middle ages.
In this case:
-Was it something common to happen?
-How would they fight regular infantry that have more numbers and are in a formation, would they be in a formation too?
-Would they use more "knightly" weapons (hammers, maces or pollaxes) or use more standard spears/polearms?
-We have many manuals teaching them on how to fight in armor against an armored oponent using grapling, would this knowledge be only intended for duels?
-And also what would knights in general (mounted or not) do in a siege?
Also english is jot my first language so sorry for possible errors.
-Was it something common to happen?
It varied with time and place. It seems to have been fairly common in western Europe in the 11th and early 12th centuries, quite rare in the 13th century, and very common in the 14th-15th centuries. I am unable to comment on practices east of the Rhine.
-How would they fight regular infantry that have more numbers and are in a formation, would they be in a formation too?
In the 11th-12th centuries, they would typically fight along with the infantry. It's not clear if they were kept together as a solid core or intermingled, but they seem frequently to have stood in the front rank, where their armor made them less vulnerable. By the 14th century, armies were increasingly composed of men-at-arms (that is, those equipped like knights, even if not of knightly rank) and archers/crossbowmen, with less well-equipped infantry in a secondary role or absent entirely.
-Would they use more "knightly" weapons (hammers, maces or pollaxes) or use more standard spears/polearms?
The weapons you describe mostly only existed during the late Middle Ages. The tools of the high medieval knight were the lance, the sword, the mace, and the axe (Anglo-Norman knights famously adopted the Anglo-Danish long axe). But all of those you mention would have been used by late medieval knights fighting on foot. Something that is not often included is the use of large lances, in most cases cut down to a more manageable length. This was very common from the 14th century on. Earlier lances were smaller and more similar to ordinary spears and could be used as such.
-We have many manuals teaching them on how to fight in armor against an armored oponent using grapling, would this knowledge be only intended for duels?
The fighting manuals described overwhelmingly date from the 14th-15th century or later and were likely intended for non-professional duelists and enthusiasts. It's difficult to know how similar they were to the personal instruction fighting men received. Beyond that, grappling in a pitched battle is not a very good idea, as it requires leaving your formation and going to ground, leaving one very vulnerable.
-And also what would knights in general (mounted or not) do in a siege?
The same things ordinary soldiers would do: stand watches, repel assaults (or lead them), sally out. I'm probably leaving something out, but it is unwise to draw too sharp a distinction between knights (and men-at-arms) and ordinary soldiers. A knight was, at least in the military sphere, simply a well-equipped, high status soldier.
Dismounting knights or men-at-arms is a reasonably common occurrence throughout the Middle Ages, especially if the army in question is English. More can always be said on the matter, so if anyone would like to address this and add to the Medieval Armies Compilation, please don't let this post stop you!
More links in next post because argh tag limit.