Re download/accessed date, I always include it because it's not unknown for sites to remove data sets or for whole sites to disappear, so it can be useful in reassuring me I'm not going mad
If I've accessed the site via the Wayback machine, I make that clear as well. And I note the form in which I consulted the source (image, transcript etc.)
I do include the website name and top level URL for the site but not the specific item (unless the site has committed to permanent URLs). And I don't include details of intermediate sites.
I don't include copyright notices -- why that and not (for example) the terms of service of the providing website? As Adrian says, it's better attached to any image that you might republish than to the source.
For newspapers I include the publication place as well to disambiguate papers with the same title and I give a column as well as page number and sufficient identification of the text in question to make the relevant article/whatever easier for people to locate. If the paper produced multiple issues on the same day, I'd include the issue information as well.
So my citation for that source would be:
London, England. "The Times" 3 April 1941 (digital images), <website name> (<url goes here> accessed: 9 Mar 2018). Page 1 Column <column number goes here> headed Deaths, entry for the Reverend Cyril Tollemache Harley Walker, of East Hanney, Berkshire, aged 57, died 31 March 1941.
I can't swear my punctuation would satisfy the most punctilious of the citation police, and it certainly isn't fully compliant with ESM, but I reckon it answers the questions: what did I consult and where and when, and how can others consult it? It doesn't presuppose that others will follow exactly the same route to the end point as I did, but does allow them to assess how likely it was that what I consulted is worth tracking down.
I'll also add I put all of it in the Title and don't use any of the other fields -- I never managed to devise a way of using them that catered for the breadth of the source types available.