PC: Margaret of Anjou as Queen of Scotland

  It could go any way.  France could get a win against England, largely driving it from the continent then have a long war against Burgundy, which it might win, lose or end in a stalemate after a long and costly conflict.  In which case Scotland could find itself very vulnerable.  Or England without a civil war could be more successful on the continent, which ironically might be better for Scotland as its facing less English forces as the bulk of the latter are in France.  In this case you could again see a stalemate with minor changes at heavy mutual costs, or either side eventually breaks to a greater or lesser degree.  Your probably not going to see a total Anglo-Burgundian victory with say the Plantagenet replacing the Valois in Paris while Burgundy get more land from eastern France but you could see some relatively minor changes of land either way.  Apart from anything else I think a French national identity, at least in its core territories around Paris and the Plantagenet's being clearly identified and identifying themselves as English is likely to be a serious barrier to that.  Basically as the Wars of the Roses showed fortunes could change very easily in such periods with battles or treachery drastically changing the relative strength of the powers.  Also possibly other external players being drawn in.  As the old saying goes no plan survives contact with the enemy - or for that matter weather, disease, chance and a multiple of other factors.

  A lot of course depends on the reaction of Burgundy and other 'French' fiefs about the continued war.  France will win in driving England from the continent because of its greater resources and the English commitments elsewhere but if there is a fear that too strong a French monarchy will threaten their own autonomy - most noticeably for Burgundy but also places like Brittany and Province say - could become involved against that.

  That's definitely an option.  Scotland would definitely like to take advantage of English weakness by raiding and possibly taking over some border regions.  Many of the Irish lords might seek to maneuver for at least more power and possibly driving the English out.  However remember this is prior to the reformation and England's OTL conversion to Protestantism so the religious issues isn't there and there are a fair number of people in the Pale who think of themselves as English since their ancestors have been there for generations in some cases so few of them are likely to welcome Gallic Irish overlords or the chaos and destruction that a conquest by them would probably bring.  The 'Old English' as they were called IIRC were generally loyal until the period after Cromwell's reconquestion as the religious issue started to override all others and they were latter largely merged into the wider Irish population.  See Normans_in_Ireland-Old_English for some brief details on them.

  As such one potential case is that everybody ends up blooded and exhausted.  Possibly even as badly as England and its possessions were by the OTL "War of the Roses".

  If instead of a civil war in England there is a great war with France [with possibly Scotland as well] and Burgundy is a co-belligerent or potentially so then such a marriage between Richard of York and the Burgundian house could seem quite favourable and more important than to tie in the Neville's to the war effort.  Or alternatively Anne could marry Edward, Prince of Wales, the son of Henry VI, which was her intended husband until he died and Warwick made his deal with the Yorkists by marrying Anne to Richard.  See Anne_Neville for a brief summary.  Although possibly if Edward survived he might be destined for a Burgundian bride as he would be the more valuable catch and also Burgundy a more important connection for him and Anne still ends up marrying one of the York house.

By 1259 England controlled almost two thirds of France so being able to reduce English control to just 20 sq miles (52 sq km) was a pretty impressive feat yes it took almost a century, but you know what they say Rome wasn't built in a day...

I think that Burgundy and France wanted control over the port, but neither dare try to take it so they just settled for English control.  There were no natural defences in the Pale of Calais so England had to establish forts and in 1558 Henri II of France was able to overwhelm these defences. The speed at which the French managed it shocked Thomas, Lord Wentworth, the Governor of Calais, that he surrendered the city. I believe that from start to finish it took the French about 7 days to take the territory.

The English Kings preferred to use the title King of France rather than the Duke of Normandy.  It would depend on the state of domestic politics as to whether the French could take the Channel Islands, but there is no reason to suggest that they couldn't have tried.

Today there is no dispute between the UK and France over whose territory the Channel Islands are, albeit they are self governing Crown dependencies.