Right, but Scotland and England had a direct border with each other and it had been a goal for sometime to see both Scotland and England united under one monarch. James I even styled himself as King of Great Britain although Parliament refused to give him the title.
Hmmm. There was a growing sense of coexistence and perhaps geopolitical brotherhood as regards Scotland, but I would be wary of suggesting that it was either inevitable or a lasting thing. Scotland largely relied on English trade to keep itself afloat and healthy, and the days of the constant Anglo-French antagonism which bred Scottish involvement in wars were gone, but there are plenty of ways that England and Scotland could have existed without deliberately sacrificing all other possibilities in order to guarantee union. There were plenty of supporters of Scottish independence, too.
I only say a split is likely because they are seperated by sea and it'd be difficult for the King to govern Norway and Denmark from London. Not saying it's impossible, but the Danes may find some resentment from being ruled from London and want their King to reside in Copenhagen.
Kind of yes, kind of no. These comments are correct, but they aren't the greatest concerns, and by themselves they are rather surmountable. The main concern is having Elizabeth choose to marry, and choose to marry Frederick in particular, of course, but it goes on from there. Denmark had been rather inward-facing for a while, concerned largely with Scandinavia, occasionally with Germany, and very rarely with anyone else. England was only just reaching a point where it was starting to look beyond western European concerns and expand political horizons to the rest of Europe. The match is possible, but it really wasn't for another generation that Denmark really opened up - as evidenced by Frederick's marrying a German from nearby Mecklemburg, and fathering a future English queen (Anne). In this regard, Sweden is a much better possibility. But let's look beyond that, because such things become non-issues if you find a way to make the match happen anyway. The more lasting issue is different.
So getting back on track, a split is entirely possible over the political distances, yes. However, the royal couple being in the wrong country isn't a crunching problem. England and Denmark particularly aren't a bad match at all because the travel distance is a mere week by medieval transport - two weeks in bad weather and you can travel by land in the same amount of time if you're desperate. It's nothing compared to the problems the contemporary Philip II of Spain created by trying to single-handedly run the entire Spanish Empire from the wrong side of the Atlantic Ocean. Norway shouldn't be considered a major issue though, since it was in essence an overseas territory of Denmark. It was run by Danish courtiers and took orders from Copenhagen. In fact those orders would probably take as long to arrive as decrees for Denmark written in London. Norway was used to delays and accepted them. Given the small journey time, Denmark would accept the delays too, as would England on the probably fairly frequent (maybe once every 6 months to a year) visits the royal couple would likely make to Denmark. It would be a disruption for sure, but in this era and particularly the century after it, bureaucracy is starting to take off. If anything, this match would make both governments better at handling business efficiently by themselves, though of course there would be teething problems for a while. The bigger issue, though, is over cooperation. On the face of it, the two countries share common ideals and styles. Both are countries somewhat overshadowed by neighbours but with significant punching power, both prefer to operate navally and are Protestant. Denmark is more Lutheran but I'd say it's feasible if not probable that the two would come to unify on a middle ground in religion - probably a middle ground significantly closer to Anglicanism but a middle ground nonetheless. However, their political spheres are totally different and that's the problem. England is interested in becoming important to the major European players - Spain, France, HRE, Austria, and to an extent places like Portugal, Italy. Denmark and beyond holds little interest factor aside from minor things like the Muscovy Company. Denmark is interested in controlling access to the Baltic, being a regional power in north Germany and trying to keep Sweden in line. There's very little overlap there. Denmark would benefit from the exposure to England's foreign policy but ultimately would lack the ability to be able to do anything except occasionally have a token part in minor skirmishes so that they could say they were there, meaning that the Danish would likely choose to ignore England's foreign policy to focus on their own affairs. England by contrast probably would have the ability to send troops to aid Denmark and be notable by the size of their commitment (it's hardly Spanish tercios, but they wouldn't be all bad) however this would be a drain on revenues and would gain England very little as it has no desire to get involved in the Baltic. This is the crunch issue. Denmark is of little use to England in the short-term at least, and England wouldn't want to be of use to Denmark. That is the real issue which could provoke a split - the two governments would both be urging a refusal to cooperate.