You'll find me to be the farthest person from a Britwanker around, for starters. As to why they give up on ousting Napoleon, the premise involves a France-wank to begin with. France is far more successful in subjugating their defeated enemies such as Austria, and butterflies lead to a more well-planned invasion of Russia supported by an engorged Kingdom of Poland, Kingdom of Hungary, Sweden, etc. that topples the Czar and turns Russia south and east of Astrakhan into splinter states due to no central authority from St. Petersburg and no realistic means for the French to actually conquer these lands. So British public perception shifts to seeming despair or resignation in toppling Napoleon's regime in Europe when the last person standing is the Ottoman Empire and thus, a shift to containment.
3. They're not doing it for the British, the French are trying to counteract Britain's naval blockade by destabilizing their economy and forcing their trading partners into the Continental System. First Russia, then the Ottoman Empire. Britain probably teeters on bankruptcy in the early years of such a scenario.
4. See above premise about a Napoleon-wank
5. Political dependency shifting into economic domination. The Ottoman Empire will be dependent on Britain to keep France on the other side of the Straights and will be forced to relocate their capital, in all likelihood. Constantinople may or may not fall, what matters is that the Osmanli dynasty doesn't collapse but are put into a precarious enough situation that they're dependent on Britain and in turn, the British are dependent on the Ottomans to sell their goods to. By the time the Ottoman Empire starts prospering on their own, their economy is intertwined with Britain's and is basically the Left Hand of the UK in foreign policy and heavily influenced by British political thought. Anti-France, pro-navy, pro-colonialism. Basically part of the informal empire in spirit. Britain isn't seizing the Ottoman Empire by any means; you're putting words into my mouth(text) and reading what you want to read. Britain 'subjugating' North Africa or Persia doesn't mean setting up a British governor.
6. Britain and the Ottoman Empire are in bed together in what starts as political dependency(ie puppet) like mentioned above, Britain isn't conquering anything. You're out of your mind if you think that's what I wrote. You think I'd call Napoleon trying and largely failing to subjugate either Russia or the Ottoman Empire impossible, then turn around and say Britain can overrun thousands upon thousands of KM from Morocco to Bengal? Really?