Thanks; so how would a bad war in Europe affect the larger British Empire? Does it weaken it enough that France, for example, can expand it's sphere?
That depends on how much the ability to maintain the Empire depended on ties to Europe. Where did they get shipbuilding materials? Where did they get food? What did they get through the Baltic? The Mediterranean? You'll have to ask someone familiar with international trade at that time.
A war between France and Austria on one side and Prussia and Russia on the other has one stumbling block.
I'm just assuming that France honors its alliance. Whether or not Russia wants to join afterwards is up to Catherine. As is the choice of sides; maybe she prefers an easier fight and joins the gang-rape of Prussia. But it would, at first, be just France and Austria vs Prussia (and Saxony).
Anyway, I would rather expect France, Britain and Russia to work together to avoid war. The French would seek to avoid a situation where they have to choose between joining a war of marginal interest to them (the real enemy is Britain) and suffering a diplomatic humiliation; the British would not want to have to finance Prussia so soon after even a victorious ARW; the Russians ended up mediating the war in OTL.
Dr Pervez, the alliance between France and Austria, traditional enemies of long standing, was active only during the Seven Years War in Europe so reversing what was called the diplomatic revolution would have had little impact on France's ability to find new allies.
Why would anyone take seriously an alliance with a power that won't keep its word? This is a matter of trust.
Also Napoleon achieved the position you raised and yet failed to defeat or even inflict serious harm on Great Britain, Hanover being seen as a burden rather than a benefit by most Brits.
I've no idea what this is meant to respond to.
I also strongly doubt that Austria would see any coalition against Great Britain worth giving Russia a free hand one or more of her own borders. The inevitable opinion of Austria would be that this benefits France and Russia but not Austria.
Whatever. Substitute Prussia for Austria or let the Russians have the Baltic. France + Russia + Spain + one of the Great Powers of Central Europe = no balance of power. Prussia was almost broken up the last time that happened.