There's a section of the FAQ dedicated to the question of how far back one could go and still communicate in English.

With your specific question of 1000 years ago, there is a famous Old English work written in that time - the epic poem Beowulf. This link shows the original text side by side with its translation. I'm not a linguist and it's possible that the differences lie partially with how language was transcribed at the time, but practically none of it is comprehensible to someone who speaks only modern English.

Probably not. It depends to whom you would like to talk to and how good you are in foreign languages, but definatelly it would still take time to learn religion, customs, way of life and new language.

Just before Norman conquest, Old English was spoken, here is wiki page about Old English in Old English, maybe try to readBeowulf, or listen to it 1 2

Old Norse would help, Celtic languages were far more common in Britain, so if you know Welsh or Gaelic, would be helpful to begin with, but without good mastery of Latin 1 guess it would be hard to find way at all anywhere in Western Christian Europe.

To understand linguistic landscape in Europe, all languages resembled each other far more, like Old Norse was closely related to Anglo-Saxon, so they would easier catch each other's words, concepts etc... but for you would be two barriers to overcome - cultural and language barrier. E.g. simple word Wednesday has ethymology from a god Wōdanaz that would be Old English "Wōden", Old Saxon "Wôdan", Old High German "Wôtan", Old Norse "Óðinn", sounds similar, and anybody from that time would possibly have some understanding of the godand why a day is named after him, while today it hardly makes a lot of sense to anybody. You would have a hard time to grasp what is happening in everyday life, you would miss sweet food and salt...

And this is some language from modern times and in English and in familiar format and theme, just couple hundred miles north of you, for comparison.

In contrast if you would be a speaker of Sardinian language, or any of Baltic languages, or Icelandic language you would probably have a lot less of those problems, because those languages did not change that much over the course of last millennium.

This would mean that you would be sent back to the year 1014; which interestingly is exactly when Sweyn Forkbeard dies and Cnut the Great is proclaimed King. More importantly, though, this is several decades before the Norman Conquest of England.

This would probably be a more fitting question for /r/linguistics. However, I can say with a good deal of confidence that you probably would not understand much at all. The variant of English spoken at this time - Old English - had yet been largely untouched by the influence of Romance languages, and of course the immense variation of space and time, that colors our English of today. It was very clearly a German language (English is West Germanic - I just mean it sounds more like German than modern English) that was basically introduced by Jute, Saxon, and Old Norse invaders. Remember that the Isles were Celtic before the Anglo-Saxon migrations.

In the above link there are some textual samples to Old English writings. Bear in mind that the letter "þ" is analogous to "th", or "d". There are some other nuances, and even though you see some familiar forms "over, the, in, of, did", in general most of it is rather close to older German (particularly in word order and agglutination; I'm not sure, but it looks like Old English combined words together, basically). Languages have English has had a naturally tendency to become simpler over time, even though its lexical base has expanded massively. The English of today has shed huge amounts of grammatical rules and conventions that were natural to Old English - and in fact most languages that were spoken a thousand years ago; conjugation, gendering, cases, double-negatives, etc. It'd be possible to render some simple sentences; "Þæt wæs gōd cyning!", for instance, if you read it out loud and carefully enunciate the words, pretty much sounds like "That was a gode (good) kin[in]g!". However this doesn't really suggest real intelligiblity; it's to be expected given that the languages are related. A good analogue is the modern language of West Frisians, which is closely related to Modern English. However if you compare the Lord's Prayer at the bottom of that page, you can see that any real mutual intelligibility is merely superficial.

More importantly is whether or not they'd be able to understand you, given the incredibly simplified structure of Modern English and its word order. You can get a feel for this sort of confusion when you take a German sentence, which I believe tends to position the verb towards the end (Mark Twain writes an amusing reflection on learning German here. Fifth paragraph is relevant) and directly translate it. You may not entirely understand what the sentence is trying to say because the sentence isn't organized in a logical way to you. But more importantly, a huge amount of our language is composed of romantic loanwords, to which these Old English people probably have almost no exposure whatsoever. One hour? Sure, you could communicate even rudimentary ideas using hand signals in an hour. But for more complex understanding, I feel like you'd be lucky to get anywhere in a month.

However, what if you dropped in about two centuries later? You'd find that the linguistic landscape was beginning to change dramatically (at least amongst the literary Anglo-Norman elite, I imagine. If anyone can reflect on whether the countryside was still composed of largely Anglo-Saxon speakers, I'd be interested to know too). Look at the development of Middle English just a couple of hundred years after the Norman Conquest. It looks like gibberish, with ridiculous spelling conventions (I believe at this time they weren't yet standardized), but try reading it slowly again and pronouncing it out loud.

"Forrþrihht anan se time comm" - "forth-right anon(?) se(?) time come"

"ben borenn i þiss middellærd forr all mannkinne nede" - "been born in(?) this middle-eard[th] for all mankind's need(?)"

"and whær he wollde borenn ben he chæs all att hiss wille." - "and where he would born been[sic] he chose all at his will"

Starts to make a lot more sense, doesn't it? Chaucer is actually perfectly readable if you approach him slowly, but I fear that escapes your time constraints a little too much. I know this stuff is already answered in the FAQ's, but I thought I'd expand on it a bit.