Increasing the fuel capacity of the Me 109 from 400L to 700L by 75% increases range about 60%. The time spent over the UK goes up much more, about 100% and the area over the US the Me 109 could operate goes up by 2-3. Twice as many Me 109 over the UK for their 2-3 times as long. That swings things quite a lot.
In Theory, yes. in practice???
Much like the Americans found out in 1943, you need a bunch of fighters operating in relays. It isn't going to take the defence (British here) very long to realise that if they engage the drop tank equipped escorts early in the flight they have to drop the tanks with useable fuel in them and thus shorten their range and endurance. Drop tanks will help the 109s considerably ( they can at least arrive over the coast with near full internal fuel ( warm and take off is always done on internal fuel) which will help quite a bit. If the British wait to engage then the operational radius does get better. But planning on being able to carry the drop tanks to near exhaustion is bad planning.
It could only occur in 1941.
Coastal Artillery had to be set up, mine fields, air superiority maintained, the German Navy built up with suitable escort vessels.
Coastal artillery not only needs to be set up, it needs to be built (or dug out of storage).
It took a number of weeks just to set the available German railroad guns. The Germans did have a number of battleship guns from WW I that were used for coastal defence.
Construction of batterie Todt was begun in July of 1940, it was not completed until Jan of 1942. It may have been capable of firing at some point in 1941.
The mine fields are a subject of debate and speculation. Both sides used mine fields in the channel for much of the war to either hinder the enemy shipping or protect their own. However local mine fields of a few kilometers or few dozen are not the same as a mine field intended to block the entire width of the channel at points removed from Dover. Coastal batteries can protect local (your side of the channel) mine fields from being swept (or raise the cost substantially). They can do very little for minefields laid near the enemy coast or in the "open" channel. The British have a huge advantage in numbers of available ships (fishing boats) available for mine sweeping.
Escort vessels covers a huge range. Many of the British trawlers were considered escort vessels, One gun capable of dueling with a submarine deck gun, a few machine guns for AA defence (rather laughable but one or more 20mms were fitted later) a depth charge rack and perhaps sonar (primitive?) and you have an anti-sub escort, rather useless if the primary threat is aircraft. British have huge advantage in numbers of destroyers so any escort vessel intended to fight them needs a much better surface armament than a trawler or minesweeper conversion. two 105cm guns vs four 4.7in isn't going to cut it. How much AA is needed depends on how well the the luftwaffe can maintain air supremacy (not air superiority)
British also have some semi-expendable C and D class cruisers.
!940 S-boats are not as well armed as the later boats. 1941 armament? The early boats had one 20mm, the pre war boats had two 20mm and many of the early war boats (or rearmed
ones had the German naval 37mm gun which was crap for this type of fighting. The Germans did have the 37mm Flak 36/37 but that required a different mount/deck space. It was done. The German 20mm guns weren't that great either for Naval AA or small craft night fighting.
Building hulls from new is going to take time and compete with the landing craft program.
and the British are doing what over the winter of 1940/41 in regards to beach defences, equipping the land army and figuring out what they need for a bitter channel fight?
Please note that the British added about 20 Hunt class escort destroyers to the fleet in 1940/early 1941, a few Black Swan type sloops and most of the N class destroyers and a few of the larger L and Ms. Four Dido class cruisers were completed in 1940 and a few more in the Spring of 1941.
While the Germans might be a lot stronger in the spring/summer of 1941 (forgoing the Russian adventure) the British would also be much stronger.
According to NAVWEAPS scharnhorsts guns had a range of 44760 yards at 40 degrees. So Scharnhorst could engage at 60% of her maximum range.
The 15 inch guns of Bismarck as (as coastal artillery firing a reduced projectile )45,932 yards (42,000 m) so one could assume that this type of gun could protect out to 30,000 yards given the infinitely better sighting, optics, range finding triangulation possible.
Land based guns can shoot accurately much further than ship mounted guns. They are not rolling, pitching and yawing and they are NOT moving hundreds of yards between shots.
however this assumes a stable land mounting, which railroad guns were sometimes not.
https://imgur.com/gallery/j7oQtkL
By 1941 the German navy would be rebuilt. It only has to keep at bay Royal Navy Motor Torpedo Boats and destroyers while the Luftwaffe deals with the Cruisers and Battle ships.
Really?
Even in 1941 the German Luftwaffe does NOT have the capability of sinking Cruisers, Battleships and Destroyers at night. Even at 20 kts the British can start and end a mission 100NM from the target area at night and have 1-2 hours of engagement time. faster speeds increase either the distance to/from bases or increase time in target zone.
While the Luftwaffe may very well dominate the air space over the invasion sites and approaches the idea they can dominate the air space over a 250-300 NM area to extent that British ships cannon be at sea in dawn or dusk conditions at the limits seems rather incredible.
The rebuilt German navy would consist of what?
Strength of the German Navy fluctuates rather widely depending on what historical missions were done or not done.