I believe that I can only answer the first half of the question - I feel as though I am not competent enough to expound on the second.
It is without a doubt that Louis XVI's plans of counter-revolution were in fact due to his disaffection with the changes to the Church, the limitations of his power, and the support from the aristocrats who supported counterrevolutionary activities. After all, the aristocrats wanted to restore the old social privilege that was dismantled during the 'peaceful' (as I will say it) years of the revolution - which they were only concerned with the fate of the King.
So the plans of the counterrevolution was this: On June 20 1791, the King was to escape from the Tuileries to Montedy near the Belgian border, part of the Austrian empire at that time. It is only from there onwards that with the aid of Marie Antoinette's brother, Joseph II the Holy Roman Emperor and the supporting émigrés would they initiate a counter revolution. Norman Hampson says that the aristocrat, especially those who supported counter revolution were primarily the émigrés, and that they were prepared for civil war and foreign invasion. Of course, as we all know how the narrative goes, a series of mishaps and failures lead to the royal family being recognised by Douret, the postmaster from Ste Menehould. After witnessing the King did he dash to Varennes to warn the guards to get him arrested.
A primary account of the escape can be read here. It also gives you a path of where they will be taking.
However, I think the most beneficial and necessary part to understand in this event is seismic repercussions it generated. Different historians give a similar, yet different response when it comes to the significance.
William Doyle for instance, states that:
“The flight to Varennes opened up the second great schism of the revolution. There had been hardly any republicanism in 1789, and what there had been abated once the king was back in Paris and accepting all the Assembly sent to him. But after Varennes, the mistrust built up by his long record of apparent ambivalence burst out into widespread demands from the populace of the capital and a number of radical publicists for the king to be dethroned.”
Similarly, Hampson states that:
"The point at issue, itself primarily constitutional, in act divided Parisian opinion along social lines, with the wealthier and more educated supporting the Assembly in its fiction that the king had been 'kidnapped' and those whom their opponents were beginning to call sans-cullotes demanding the kind of clear and forceful measures that corresponded to their view of the situation. Inevitably ,therefore, the pursuit of a compromise with the king led the Assembly to prepare for conflict with the sans-cullotes, who were organizing petitions against any hasty rehabilitation of Louis XVI."
Other effects was the repudiation of the direction of the Revolution and many of the acts Louis XVI previously endorsed. Louis XVI himself was humiliated, compromised ad discredited Louis XVI. It showed not only did he misread the political situation of France, but one may also argue that it was the first steps into Republicanism and radicalism. After all, it was at this point at time that ministers became divided over the punishment of the King. Others called for Republicanism, others still wanted to maintain a sense of monarchy, and others called for his abdication.
One of the reactions can be seen in writing expressed by figures such as Abbe Greogire, who was in the now torn-apart Jacobins, argued that Louis XVI should be forced to abdicate:
"The premier public servant abandons his post; he arms himself with a false passport; after having said, in writing to the foreign powers, that his most dangerous enemies are those who pretended to spread doubts about the monarch's intentions, he breaks his word, he leaves the French a declaration which, if not criminal, is at least -however is envisaged - contrary to the principles of our liberty. He could not be unaware that his flight exposed the nation to the dangers of civil war; and finally, in hypothesis that he wished only to go to Monmedy, I say: either he wanted to content himself with making peaceful observations to the National Assembly regarding its decrees, and in that case it was useless to flee; or he wanted to support his claims with arms, and in that case it was a conspiracy against liberty."
So evidently, the effects would only lead to one even to another. After this issue would this lead to the Champ de Mars massacre - something that would generate a deeper schism between the nation. It is noted that the outcome of Louis XVI's plans to escape were far more traumatising than what I wrote above, but, if you were to put the effectiveness of the plan in terms of the context of what the King faced back then, it proved to be not realistic at all. After all, Louis XVI's miscalculations accentuated any sense of antagonism against the monarchy, and it would only be his downfall. He will be later be known as 'Citizen Louis Capet' in the minds of the many. More importantly, a betrayer to his country and the revolution.
If you were you view if it was realistic in contemporary sense however, I think that can be answered by other more competent historians here.
Sources:
Doyle, W 2002, The Oxford History of the French Revolution
Hampson, N 1963, A Social History of the French Revolution
McPhee, P 2002, The French Revolution
edit: Just a question I wanted to ask the others reading (since I wanted some feedback) - is there any way you suggest for me to improve an answer? I'm learning to how write more academically as a high school student here. It's definitely not as top notch as compared to what goes on here, but I'm eager to improve. Hope this question doesn't derive the question OP asked!