Whst if England from 1065 AD moved to 476 AD?

  That would be interesting.  At this point England is potentially in for a period of fairly stable government, especially since the Normans and Danes have gone and there's no alternative threat, other than possibly the down-time Anglo-Saxons.  England does have a system for defence built up during Alfred's rule against such raids, although it later failed under Æthelred's weak reign.  With Edward already faltering and a political if not military crisis due to the effective change in date Harold is almost certain to become king.  The northern lords will be potential rivals while I'm not sure what Wales and Scotland were like at this time so probably some problems there with raids at least.

  England would probably become a centre of learning but how much difference between the Catholic churches of 476 and 1065 in organisation and doctrine I don't know.  Coupled with the fact that western Europe is being overrun by Germanic groups which are either Arian or pagan [Franks and whatever happens to the Anglo-Saxons].  OTL the English had done a lot of Christianize the low countries and Germany in earlier centuries so they might try this again here, along with Frankish lands and possibly some efforts against the Arians but they could find it more difficult than the OTL conversions as non-Christian beliefs are still strong at the moment.  How successfully relations with Rome are established would be a big issue. 

  England will have lost a lot of its trading contacts with neighbours, by land and sea and they have load their population in the Lothian region so regaining that could be more difficult.  However England should have an organizational edge over most of its neighbours, at least in Britain.  They have lost their fairly decent relations with Ireland however as that's still pretty much fully pagan.

  By this point and with Danes across much of the north and east and Norse in part of the NW they will probably know about Greenland as well and possibly have at least some rumours of Vineland.  Suspect that events to the south and east are likely to keep them pretty busy for quite a while.

  On your questions:

a) Three-field_system - it says that it was developed in China and and was adopted in Europe in the medieval period, which it classifies as the 5th to late 15thC so could be either way.

b) Heavy_plough - actually says "General adoption of the carruca heavy plough in Europe seems to have accompanied adoption of the three-field system in the later 8th and early 9th centuries, leading to improved agricultural productivity per unit of land in northern Europe" which suggest that both the heavy plough and the three field system should be available in England.

c) Horse_collar#History - states for the final version of it "The horse collar eventually spread to Europe c. 920 AD, and became universal by the 12th century" & a bit further down "Following the introduction of the horse collar to Europe and its use being clearly evident by 1000 AD" so there is a decent chance that it would be known by at least a few in England by this time. 

  One other political/religious fact they will know about will of course be the rise of Islam but how that and the expulsion of Christian power from its richest and most ancient territories in the ME will have on religious ideas I don't know.  The idea that the patriarchates of Jerusalem and Alexandria will be lost - plus Antioch only fairly recently having been regained by the eastern empire - which is of course in schism with Rome from 1054 I don't know.  Along with the loss of the rest of N Africa and most of Iberia.

  Good point on trade in that the English will have ships some way in advance of anything else at this point.  Also I'm not sure about their contact with Byzantium but their very familiar with trips to Rome and other areas, albeit in a radically different political and religious situation.  Mind you I think most of those trips were by land rather than sea.

  In terms of pagans at this time they were all of Scandinavia along with the Low Counties, all we now think of as Germany and assorted other areas.  Ultimately they will almost certainly be conquered by Christian states as the latter are simply more organised and intolerant overall.  At this point however the bigger issues are likely to be differences between 1065 England and the 476 church and also the large numbers of Arians politically dominant across much of the former western empire and chunks of the east.

  I think the Danish rather than the Norse had much larger influence and blood connections in England, or are you referring to Norse as a generic term for Vikings/Scandinavians.  I was using it in terms of the Vikings who chiefly came from Norway.