Two objects that I find very interesting related to this are a pair of viking-age skulls in the National Museum of Ireland. This one that was found in conjunction with iron chains, and had about twenty superficial cuts and nicks on it, and this one which has had a considerable part of the skull itself cut off.

Anyway, I think a quite good text to look at would be Usamah ibn-Munqidh's 'Kitab al-I'tibar'. It's from two and a half centuries before the time-period you're asking about, so the descriptions of armoured combat are not going to be that helpful, but I think it's quite useful in a number of ways (note, I'm copying all the quotes from Philip Hitti's translation 'An Arab-Syrian Gentleman and Warrior in the Period of the Crusades' because it's free on the internet, but if you want to read it yourself I'd recommend Paul Cobb's more recent translation 'The Book of Contemplation' first; the style is a lot more readable, and the Arabic transliterations are more modern).

The thesis of Usamah's work is that the future is set by God, and, basically, that really strange things happen. You can't predict what will happen (or, in your case, define a baseline of what 'mundane' and 'believable' looks like), because real life is weird: sometimes people are killed by as scratch, sometimes they survive extremely serious wounds. He illustrates this idea with a series of stories about exceptional occurrences, mostly drawn from his own, very long, life. A lot of the stories are about warfare, and very applicable to this question.

To answer "how deeply would a sword...pierce an unarmored body?":

The crushing of the head of that old man (may Allah's mercy rest upon his soul!) by the mangonel stone has brought to my mind stories of blows administered by sharp swords. Here is one of them. One of our comrades, named Hammām al-Ḥajj [the pilgrim] had an encounter with one of the Ismā'īlites, when they attacked the Castle of Shayzar, in a portico of the residence of my uncle (may Allah's mercy rest upon his soul!) The Ismā'īlite held in his hand a dagger, while al-Ḥajj held a sword. The Bāṭinite rushed on him with the knife, but Hammām struck him with the sword above his eyes. The blow broke his skull, and his brains fell out and were scattered over the ground. Hammam, laying the sword from his hand, vomited all that he had in his stomach, on account of the sickening he felt at the sight of those brains.

On that day I had an encounter with an Ismā'īlite, who had a dagger in his hand, while I had my sword. He rushed on me with the dagger, and I hit him in the middle of his forearm as he was grasping the handle of the dagger in his hand and holding the blade close to his forearm. My blow cut off about four inches of the blade and cut his forearm in two in the middle. The mark of the edge of the dagger was left on the edge of my sword. An artisan in our town, seeing it, said, "I can remove this dent from it." But I said, "Leave it as it is. This is the best thing in my sword." The trace is there to the present day. Whenever one sees it he knows it is the trace of a knife.

(page 146)

"How about an armored one?" The armour of Usamah's day was mostly mail shirts, and the 'khuzāghand', a mail shirt, or sometimes two, sewn into a padded garment (Muslim warriors of the day also sometimes wore short lamellar corselets, but Usamah never mentions them).

One of their [the Franks] horsemen hastened to me, displaying his colors in a green and yellow silk tunic, under which I thought was no coat of mail. I therefore let him alone until he passed me. Then I applied the spurs to my mare, which leaped over the wall, and I smote him with the lance. He bent sideways so much that his head reached his stirrup, his shield and lance fell off his hand, and his helmet off his head. By that time we had reached our infantry. He then resumed his position, erect in the saddle. Hav ing had linked mail under his tunic, my lance did not wound him. His companions caught up with him, all returned together, and the footman recovered his shield, lance and helmet.

(page 90)

On the other hand however:

One of our troops, a Kurd named Mayyāḥ, smote a Frankish knight with a lance, which made a piece of the link in his coat of chain mail penetrate into his abdomen, and killed him. A few days later, the Franks made a raid against us. Mayyāḥ, who had just been married, went out to meet them with full armor but wearing over his coat of mail a red garment of his bridal clothes, making himself especially conspicuous. A Frankish knight smote him with a lance and killed him (may Allah's mercy rest upon his soul!).

O, how close to his funeral was his wedding!

(page 76)

"What kind of wounds did they leave, and how treatable were they?" This is another of Usamah's pet subjects, strong men being killed by wasp-stings, and others surviving terrible wounds, but I'll give one example:

The second morning, as I was standing in Bandar-Qanīn, a village near Shayzar, I saw three persons advancing, two of whom looked like human beings, but the middle man had a face different from the faces of human beings. When they came near us, behold! the middle man had had his face struck by the sword of a Frank in the middle of his nose and cut as far back as the ears. One half of his face was so loose that it hung over his chest. Between the two halves was an opening almost the width of a span. With all that, he was walking between two men. In this condition he entered Shayzar. The surgeon sewed his face and treated it. The sides of the cut stuck together, the man recovered and returned to his previous condition and finally died a natural death on his own bed. He used to deal in beasts of burden and was nicknamed ibn-Ghāzi al-Mashṭūb. His nickname al-Mashṭūb [the gashed one] he acquired as a result of that cut.

Let no one therefore assume for a moment that the hour of death is advanced by exposing one's self to danger, or retarded by over-cautiousness.

(page 193)

There's a lot more of this stuff: notable wounds, miraculous escapes, unexpected victories and so on, basically all the most atypical and unusual stories he knows related to war (and a lot of very similar material about hunting). It's well worth reading for interest, but it's probably not worth putting in a book: no one would believe you.