TL;DR: It was rare for laity to be able to read and write; everyone carried a knife but generally only nobility and soldiers carried weapons; Scott mentions the writing materials in chapter V because they will be used in chapter VI; the writing materials included parchment, quills and ink.
Was it rare to be able to write?
It depended on which section of society you belonged to. Ivanhoe is set in 1194, during the reign of Richard I. At that time, it was a stereotype that clergy were literate and laity illiterate:
The ancient notion of three estates with distinctive functions was well known in medieval England. The clergy prayed, the knights fought, and the peasants laboured. In this tripartite scheme, literacy was seen as the distinctive skill of ecclesiastics; indeed, in the French and English languages, the word ‘clergy’ meant not only clerks but written learning. Those who practiced it were clerks, and ‘lay’ was a synonym for ‘illiterate’.
Nicholas Orme (1996). ‘Lay Literacy in England 1100–1300’. In Alfred Haverkamp & Hanna Vollrath (eds.), England and Germany in the High Middle Ages, Oxford University Press.
Scott included an episode in Ivanhoe illustrating this stereotype:
“Let us see the cause of this cursed clamour,” said Front-de-Boeuf—“here is a letter, and, if I mistake not, it is in Saxon.”
He looked at it, turning it round and round as if he had had really some hopes of coming at the meaning by inverting the position of the paper, and then handed it to De Bracy.
“It may be magic spells for aught I know,” said De Bracy, who possessed his full proportion of the ignorance which characterised the chivalry of the period. “Our chaplain attempted to teach me to write,” he said, “but all my letters were formed like spear-heads and sword-blades, and so the old shaveling gave up the task.”
“Give it me,” said the Templar. “We have that of the priestly character, that we have some knowledge to enlighten our valour.”
Walter Scott (1819). Ivanhoe, chapter XXV.
(The use of ‘Saxon’ here and elsewhere in the book seems wrong to me—the English had called themselves ‘English’ since before the Conquest, and the Anglo-Norman word was ‘Engleis’. Possibly Scott used ‘Saxon’ deliberately as a defamilization device.)
However, the rule that only clergy could read and write was far from universal, and the 12th century was a time of increasing literacy among the laity. In the case of the royal family:
In the twelfth century at last it was becoming common to put the prince to letters in his youth. Henry I accurately dates the change, for though all the children of William the Conqueror seem to have received some formal education in youth, he alone impressed his contemporaries as an educated man. [… By the 13th century,] all our kings were taught letters in their youth, and their literacy, as distinct from their culture, has no particular importance. The change is reflected in the silence of the chroniclers, which seems to assume an education in letters.
Vivian Hunter Galbraith (1935). ‘The Literacy Of The Medieval English Kings’. Proceedings of the British Academy vol 21, pp. 202–5.
So the situation as of 1194 was that a lay member of the nobility would not be expected to be literate, but it would not be very surprising if he were; whereas it would be rare to meet a yeoman or peasant who could read and write. The situation was very different among the Jews, who needed to be literate in order to study the Torah:
At least up to 1200, they were culturally superior to virtually all their Christian contemporaries. Whereas cathedral schools might educate a small minority of (male) clerics, European Jews, in England as elsewhere, inherited and continued a much more universal instruction in literacy, numeracy, and the handling of legal texts, which often involved women as well as men.
John Edwards (2003). ‘The Church and the Jews in Medieval England’. In Patricia Skinner (ed.), The Jews in Medieval Britain, Boydell Press.
In Ivanhoe, Isaac of York was certainly literate in Hebrew (this is mentioned in chapter VI), probably in Arabic (his daughter Rebecca reads a message “in the Arabian character” in chapter XXXVII), and possibly in Latin, Anglo-Norman, and English too.
Why “a small knife, but no weapon”?
To make sense of this phrase, you have to understand “weapon” as meaning “weapon of war”, that is, a sword, spear, mace, or something similar. Of course a knife can be used as a dagger, but many objects can be used as improvised weapons.
In medieval England, most men, and many women, carried a knife for daily tasks like food preparation. When a host gave a meal, his guests were expected to bring their own knives. In Ivanhoe, Isaac of York would have used his knife to cut the nibs of his quill pens, sharpen them regularly as they wore down, trim his parchment, score lines, and scratch out mistakes.
Why mention the writing materials?
So that when Isaac uses them in the next chapter, we don’t need to wonder where he got them from:
“No more of that,” said the Jew, changing colour; and drawing forth his writing materials in haste, as if to stop the conversation, he began to write upon a piece of paper which he supported on the top of his yellow cap, without dismounting from his mule. When he had finished, he delivered the scroll, which was in the Hebrew character, to the Pilgrim […]
Scott, chapter VI.
The difficulty of acquiring writing materials furnishes a plot point:
“And who shall bear such a message?” said Front-de-Boeuf; “they will beset every path, and rip the errand out of his bosom.—I have it,” he added, after pausing for a moment—“Sir Templar, thou canst write as well as read, and if we can but find the writing materials of my chaplain, who died a twelvemonth since in the midst of his Christmas carousals—”
“So please ye,” said the squire, who was still in attendance, “I think old Urfried has them somewhere in keeping, for love of the confessor.”
Scott, chapter XXV.
What were these materials?
Isaac must have carried:
Parchment. Scott writes ‘paper’ in Ivanhoe but that’s anachronistic: paper manufacture didn’t come to England until a couple of centuries later. Parchment is the depilated, scraped and dried skin of animals, usually sheep and goats; the finer quality skin of calves is known as ‘vellum’.
Quills. Scribes made their own pens from feathers, most commonly from geese. This video by Bernadette Banner shows how a nib is cut. Quill nibs wear down quickly and have to be sharpened regularly:
John of Tillbury, one of the scholars in the household of Thomas Becket in the twelfth century, describes how a clerk taking dictation would need to sharpen his pen so often that he had to have sixty or a hundred quills ready cut and sharpened in advance.
Christopher De Hamel (1992). Scribes and Illuminators. British Library.
Ink. Scribes made their own ink from oak galls and ferrous sulphate, or from lamp black and gum arabic. The processes were time-consuming, so a traveller like Isaac would have carried a supply in an inkhorn, an inkwell made out of animal horn with a lid.
He might also have carried:
An awl, for extracting the internal membrane from the feather; for pricking holes in sheets of parchment; and for pinning the parchment to a desk to hold it in place while writing.
A ruler, for making straight margins and lines.
Sealing wax, for closing letters.