You're right, this is a difficult question to estimate. Unfortunately, so are your other ones! We simply don't have the data to give a solid quantitative answer for things like the number of books or the literacy rates. Additionally, it's impossible (and really not very useful) to generalize on a global level about things like literacy. Here are some things to consider, though, that get at your question in a roundabout way, at least for Europe.

First, what were libraries in the Middle Ages? In western Europe, they were overwhelmingly monastic. Cathedrals and courts also kept texts, but not anywhere near as many as the monasteries. Monks produced texts for their own use as well as for their patrons in their scriptoria. The texts they produced for themselves tended to be religious (Bibles, liturgical texts, etc.), but they also copied classical texts to use for language study - mostly Latin, but also Greek. Monastic libraries are to thank for the preservation of classical literature after the decline of the Roman Empire, especially Irish monks, who didn't have as much structural decline as continental Europe with the withdrawal of Roman troops, administrators, and money. The biggest non-monastic library in the former Roman world that survived to 1000 AD is the Library of Constantinople, which was the imperial library for the Byzantine Empire. It focused much more on ancient texts than European monasteries did, and it maintained a large staff of scribes who copied out ancient texts to preserve them. Unfortunately, the Library of Constantinople was damaged several times, including in 1204, when it was attacked by European crusaders on the infamous Fourth Crusade. So while it certainly existed in 1000 AD, it had a rough existence afterwards.

So precisely what kind of texts were monks interested in? We don't have a lot of catalogs for monastic libraries, but the ones we do have indicate an interest in commentaries on scripture, the church fathers, monastic texts like the Benedictine rule and commentaries on it, the writings of great popes like Gregory the Great, sacramentaries (guides for how to conduct the sacraments), law texts (especially canon law), necrologies (lists of members of the monastery who died), martyrologies (lists of feast days), saints' lives, charters (which they sometimes forged if the original had been lost), histories, and many more.

Literacy rates are also impossible to state with any precision, but we can talk about literacy in a general way. First, it's important to keep in mind that literacy is not really a very well-defined concept. Does literacy mean being able to read at a certain level? Being able to read silently? Being able to write as well as read?

As I said before, monasteries were very much the bastions of the written word in the post-Roman period, both in terms of the physical documents themselves and in terms of the skills of reading and writing. So when, in the late 8th/early 9th century, Charlemagne wanted to increase literacy throughout the Frankish kingdoms, he turned to the monks. This period, which is known (somewhat contentiously) as the Carolingian Renaissance, saw the increased use of the written word for administrative purposes, the development of a new and more legible style of writing, and the establishment of schools in monasteries, cathedrals, and the palace itself. Ideally, the schools were meant to be open to any child who wanted to learn (male or female). In practice, this still meant primarily the children of nobles. Nevertheless, the infrastructure was put in place to expand literacy outside of the monastery.

Coincidentally, the year 1000 AD comes right after another supposed renaissance, the Ottonian. Otto I, king of what's now Germany, was crowned emperor by the pope in 962. He was the first of what would come to be known as the Holy Roman Emperors. With the revival of the imperial Roman title came a renewed interest in Roman heritage and therefore something of a revival in classical texts. This period sees the flourishing of some of the greatest monastic scriptoria like Hildesheim and Reichenau. Later on in the Ottonian dynasty, Otto III took a deep interest in Byzantine culture, thanks to his Byzantine mother. You can look at the Reichenau Gospels here and see some of the combined classical and Byzantine influences in the decoration.

Monastic reforms in the 10th century in both France (at Cluny) and Germany (at Gorze) also brought increased monastic patronage and swelling numbers of monks.

At the turn of the millennium, writing was also being used increasingly in administrative contexts. We can look at the Domesday Book (a list of properties and their values produced right after the Norman Conquest of England in 1066) as an example. Writing was moving out of an exclusively religious context in this period, and we can assume that rising literacy rates accompanied that shift.

So around 1000 AD, you have a renewed interest in classical texts, increased patronage of monasteries, more monks, and the increased use of writing in royal administrations. Clergy and monks (and nuns!) could likely read and write to a certain degree. Among the laity, it's harder to say, and again, percentages are impossible to offer with any kind of accuracy. Cheryl Glenn has a nice introductory article on the kinds of literacy in the Middle Ages, though. Charlemagne, for instance, could read but not write, since he started learning too late to achieve the coordination. Margery Kempe, an English mystic (or possibly kook) in the fifteenth century, couldn't read or write and yet composed her autobiography by dictating to someone who could.

For further reading: Cheryl Glenn, "Medieval Literacy outside the Academy," College Composition and Communication 44/4 (1993), 497-508. (for modes of literacy in the Middle Ages)

Steven Runciman, Byzantine Civilization (for the Library of Constantinople)

Rosamund McKitterick, The Carolingians and the Written Word and The Use of Literacy in Early Medieval Europe

J. Coleman, "A medieval Irish monastic library catalogue" The Bibliographical Society of Ireland 2/6 (1925), 111-120. (for an example of a library catalogue - but be warned, this one's quite late)

Edited for formatting