How did various continental secular authorities, Protestants and Catholics feel about these events given that England was such a powerhouse at the time?
This is a pretty huge question but I can hopefully answer it to some extent at least.
Firstly, its worth pointing out that at in the period in question, England actually wasn't really all that much of a 'powerhouse'. They were a notable European kingdom and were not insignificant, but England was not really as powerful militarily as Spain, France, or even probably the United Provinces of the Netherlands in this period, and would not really have much ability to project power either in Europe or the wider world until after the Revolution of 1688. Neither had the English economy really started to show the strength it would show in the 18th century yet.
Many of the European states were also involved in the Thirty Years War at this point, meaning that English affairs were not really a huge concern to many on the continent.
That said, there were certainly connections between the English Civil Wars and the Thirty Years War, and many of the same political and religious issues were at play in both, so here goes:
Although serious fighting wouldn't really break out in England for another three years, the English Civil Wars (more accurately called the Wars of the Three Kingdoms as fighting also occurred in Scotland and Ireland) actually began, for all intents and purposes, in Scotland in 1638. King Charles and his religious allies had hoped to impose a 'Book of Common Prayer' on Scotland to bring its religious practices closer to that of England.
However, the Scottish Presbyterian Kirk was very strong and many Scottish nobles and intellectuals had a very particular, limited concept of Kingship which had emerged from their reformation, which in contrast to the English reformation, was centred around the aristocracy rather than the King. The imposition of the Prayer Book was seen by the Scots as both an affront to their church, and as an attempt by Charles I to overreach his royal authority.
The Scots agreed a 'National Covenant' via which they swore to defend their religion and nation, and while this document, as with most acts of resistance in this period, blamed the King's advisers rather than him, it effectively meant that the Scots were at war with Charles's England.
Charles raised an army to fight the Scots, and two expeditions were attempted against Scotland in what became known as the 'Bishop's Wars' (because the Presbyterian Scots rejected bishops). Neither of these were successful and the war petered out with the few battles that took place mostly won by the Scots. The cost of raising the army proved devastating for Charles though, and is one of the reasons that Charles needed to recall Parliament, leading to the English Civil Wars.
Now, this is where the Thirty Years War comes in. Charles had relatives in the Palatinate of the Rhine in Germany, which was involved at various points in fighting against the Catholic side in the TYW. This meant that he had for a long time faced strong pressure from Protestants at home to provide aid to the Palatinate.
However, the rebellion in Scotland complicated this picture a lot. Scotland had a close relationship with Sweden and the Netherlands due to them all sharing a reformed, Calvinist version of Protestantism, and they provided the Scots with arms with which to resist Charles. Sweden and the Netherlands were also on the opposing side to Spain in the TYW. On the eve of the Civil Wars, therefore, Charles was moving towards an alliance with Spain, but this made his relationship with the more anti-Catholic English Protestants, many of whom would ultimately come to fight against him in the Civil Wars, even more fraught.
So essentially, the wars in the three British Kingdoms were a sideshow to the European powers as long as the TYW went on, but there were overlaps and connections between the two. Charles was faced with a dilemma of balancing his strategic interests with the fact that many in England supported the Protestant side in the TYW, many members of which were supporting Charles's enemies in Scotland. This was one factor, along with several others, that contributed to the breakdown in relations between Charles and many of his more reformed or puritan leaning protestant subjects.
Now, as for the relationship between Cromwell's England and other powers, I actually wrote a little bit about this recently: