1 - If the Chinese "lob" a nuke at London and we cannot respond, why should the US Risk MAD (and its total destruction) by retaliating on our behalf? This type of scenario has been argued at length and the conclusion is always the same. A Nuke power will not Nuke a fellow Nuke power in retaliation for a Nuclear attack on a non-Nike power.
It is quite easy to find out how many Trident boats are at Faslane. If you want to go low tech, you just turn up and watch. If you want to go hi-tech you can use a satellite picture. When they sail out from Faslane it is a very public operation. In a crisis situation this would be unacceptable.
I think it fair to say this counters your point here.
2 - Agreed, I see no reason why we should not be on cordial terms with China. However, we are talking about a hypothetical scenario here. In the medium term we do not know who will possess the capability to attack us with Nukes. China are one of a number who currently possess that capability, other states such as North Korea and Iran may possess that capability in the future.
Do remember that the UK's foreign policy will be very similar to the US's on certain issues such as N.Korea, Iran.
3 - Of course the Vanguards were not solely responsible for Cold War security. In fact, they came after the end of the Cold War. It is generally acknowledged that Nuclear weapons prevented the Cold War from going hot, and the UK arsenal will have played its role in this regard.
I accept that we have moved on from the Cold War, however the world is arguably more dangerous now than it was 25 years ago.
4 - with Tomahawks, the key is that they can be shot down. The whole point about Trident, and ICBM/SLBM's in general, is that they cannot be stopped. Provided both sides know that, and there is no uncertainty about that fact, stability is maintained. If one side thinks it can attack another and then defend its self from reprisal, there will always be the temptation to strike. In the hands of someone irrational, that is a dangerous combination.
Whilst Cruise Missiles can be "nuclear weapons" they cannot perform the function of a "deterrent".
I have no info on how many Tomahawks have been shot down, but I suspect the answer is greater than 1.
5 - Nuclear weapons are useful with rogue states, as a shield but not a sword. An established state would (or rather should) never launch a first strike on such a state. However, if future dictators sitting in Pyongyang, Tehran or wherever know that their cushy lifestyle can be wiped out in an instant, it will force them to exercise an element of restraint, which can only be a good thing. If they know they could Nuke the UK without our being able to do anything about it, they might use that against us (diplomatically and politically I mean).
6 - yes it is a status symbol. It is proof that we as a nation are prepared to guarantee our territorial integrity. Without this we would not still be considered a major world power.
7 - there is a threat from existing nuke states, because they are capable of attacking us. The relevant question is, are political and military circumstances such that they would chose to use that capability and attack us?
Right now I think the answer to that is no. the two main variables of this are that 1 - there is no reason to attack us, and 2 - we could retaliate. Whilst the circumstances in point 2 are fully under our control, the circumstances in point 1 are not entirely in our control and may be affected by the answer to point 2.
For all these reasons I expect Trident to be renewed.
I think I can see what you are trying to get at, however the arguments as to the relative Merits of Trident as a deterrent have been argued and discussed at length in the highest elements of government. The Trident system comes out on top.
What you need to do is convince myself and others that we will not need a nuclear deterrent in the next 50 years, and that is something you can never prove, only speculate.
Again, if Trident is not renewed it will be for economic reasons only.