Heretical though it may be - I will say that there is no right way to do a citation. Only useful ways. What is useful to me, may not be useful to someone else. In addition, if they are read by someone totally ignorant of the topic, they will be useless.
So - a couple of comments first.
That Wikipedia reference appears to be what you'd put in a Wikipedia article. The ONS reference is - to me - a nonsense. ONS are not the publishers of the (FreeBMD) source. They published the source of the source.
Just because a slot is there, doesn't mean it has to be filled in. Your citation appears to have 4 references to FreeBMD - plus the URL. Even Elizabeth Shown Mills encourages us not to repeat things unnecessarily. The art is knowing what to omit - trial and error will help.
Here's what I did:
- I created a new Source for this entry, as my previous entries in my trees use obsolete titles. Note that I use a different person than in your case.
I have omitted the Author (FreeBMD), leaving the Publisher as FreeBMD, because I didn't want too much repetition. Personal choice.
(If entered, the Author is FreeBMD, not the GRO. The GRO created the original index. FreeBMD is a transcript of that, and the convention is that, because of the possibilities of errors, the Author for a transcript, extract, summary, etc, is the creator of the transcript, extract, etc. The GRO is the author of the original, which is why it's important to be able to see the source of the source, which you can, in that Note.)
The Note describes the "source of the source" - I have just written "Citing original indexes from GRO" - feel free to expand that if it's more meaningful to you.
Repository is "FreeBMD web-site" - having "web-site" may be felt to be pointless.

- Here's my Citation stuff. Remember, a Citation is supposed to do things like say, "Where within the Source is it?" and "How does it relate to the event the source is justifying?" (E.g. primary info, etc.).
My interpretation, based on the instructions on the screen, is that "Where within Source" needs to go in Detail (Required). "Where within Source" is a simple page number in a book - here you ought to enter the search criteria details. But the search criteria are contained in the transcription so why repeat? (If your reader doesn't understand using FreeBMD, they need a training course, not your citation...). So here I entered just "Death Indexes" which is, short of the entire search criteria, about the only choice you can make en route to the data.
Transcription should contain just that. It's the most important thing - it's what you find when you get there. There's a horrible tendency people have of putting District, Volume and Page, etc, in against FreeBMD as if they are references for how to find the index. They're not. They're references for how to find the actual certificate.
Web Address - I just put the address of the web-site. Some people will put the URL of the index entry but there is no guarantee that FreeBMD won't change its URLs. You should be abe to find the index entry again from the transcript.

So finally it looks like this:

I would contend that to anyone who understands FreeBMD, they can use my resulting Source Citation to find the record again.
What's Missing: Primary / Secondary / etc, should presumably go in Other Information against the Citation.
This is one where Ancestry's scheme creaks because of the ludicrously vague nature of Detail(Required). The above is the result of several comments back and forth.