The Jew-loving Nazis of Scenario 1 seem like a pretty big departure from the Nazis we know and love, but yes, if the Germans had got the bomb things would have worked out differently.
I don't buy Scenario 2. The loss of Britain would have made bombing Germany difficult, not impossible. Worst-case scenario is that they have to develop a long-range bomber. More likely they'd have invaded some part of Europe or North Africa (most likely Britain itself) as a first order of business upon entering the war -- I doubt they would have made it to 1945 without a well-defended slice of Europe. Of course this scenario probably also has a non-negligible Luftwaffe defending German cities in 1945 but, heck, the nukes have gotta get through eventually.
I'm not sure your second scenario is as quickly solvable as you think. The loss of the uk would have been the loss of an important strategic platform - essentially allowing a second front to squeeze Germany from when it came to attack. Also it would have given Germany pretty consolidated control of our side of the North Atlantic, supply routes would have been severely disrupted.
I think ultimatelythe war would have been won but redeploying to, say, North Afric would have taken a while.
I don't buy Scenario 2. The loss of Britain would have made bombing Germany difficult, not impossible. Worst-case scenario is that they have to develop a long-range bomber. More likely they'd have invaded some part of Europe or North Africa (most likely Britain itself) as a first order of business upon entering the war -- I doubt they would have made it to 1945 without a well-defended slice of Europe. Of course this scenario probably also has a non-negligible Luftwaffe defending German cities in 1945 but, heck, the nukes have gotta get through eventually.