The attack on the Gallipoli peninsula was a brain child of Winston Churchill, though he was not the only one promoting the campaign and there have been many other leaders in military and politics who faild miserably, starting with Lord Kitchener himself.
Besides the consequences to his political career, how did Churchill later deal with Gallipoli? I have never read his autobiography (it's on my to-read list since 2 decades or so) or any biography about him.
Did he take over the responsibility?
Did the campaign influenced later decisions in WWII?
How, if ever, did he deal with the moral implications of his idea to open up a front in the "backyard" of Germany and Austria which lead to the loss of a quarter million soldiers and seamen?
I only know a bit of Churchill regarding his time as Prime Minister in WWII, read some of his famous speeches, but can't recall if Gallipoli was mentioned.
I can't answer all of your questions but some I hope I can answer.
The attack on the Gallipoli peninsula was a brain child of Winston Churchill
We first, have to look at this a bit closer. While opening another theater of war, was Churchills idea, simply saying that 'the Gallipoli compain' was all his responsibiltiy is not really correct. What happend in Gallipoli was never really planed or imagend, not by Churchill, not by anybody else.
Churchills idea was to take a huge fleet of aging ships, and a few newer once to force the way into the black sea. The rational for this was that the turks would be suprised, they could be split, that the ruissans could easly trade with the english and the french. So Churchill saw it as a low risk, high gain operation. In the worst case you lose a lot of aging ships that you don't really need (because the main fleet does a fine job containing the german navy), in the best case you knock out a opponent, get communications running within your alliance and beeing able to attack austria. Infantery would not be used all that much.
So form the outset, this is not really a terrible idea. I think that it was even a pretty good idea.
However this kind of vision, had to deal with many practical problems. Some of them politcal, some with the weather and many other things. I don't really want to go into all of these, since you are many interested in Churchill. Churchill for all his position, can not direct what is happening on the ground. He could try to persuade the general on the ground to be more offensiv or something like that.
Things keeped dragging on and events spinned out of control, in the end producing results that nobody really wanted. The army go involved and sent troupes to help. The Navy commanders lost overall control on the ground. Politically a lot was happening in england, practically Churchill had lost any controll he ever had over the events. I think the term 'throwing good money after bad' is quite suiting. Instead of trying one for strategic success with limited resources, they keeped doubling down.
Churchill was blamed for the overall disaster. However its hard to lay the majority of the events at his feet, he was the prime mover, but events spinned out of his control. Later reports show that many people had made mistakes. Churchill had some, but others had made very bad errors as well.
Did he take over the responsibility?
No. He defends himself with some of the same things I said above. He had many more things to say but I think the main point, I have made above. His idea was to use old ships in a suprise attack, high gain, low risk.
I hope somebody that knows more, can give a better answer.