Why doesn't Wikipedia require everyone to use exactly the same style for formatting citations on every single article, regardless of the subject?
Different academic disciplines use different styles because they have different needs and interests. Variations include differences in the choice of information to include, the order in which the information is presented, the punctuation, and the name of the section headings under which the information is presented. There is no house style on Wikipedia, and the community does not want to have the holy war that will happen if we tell people that they must use the style preferred by scientists in articles about history or the style preferred by artists when writing about science. Editors should choose a style that they believe is appropriate for the individual article in question and should never edit-war over the style of citations.
What styles are commonly used?
There are many published style manuals. For British English the Oxford Style Manual is the authoritative source. For American English the Chicago Manual of Style is commonly used by historians and in the fine arts. Other US style guides include APA style which is used by sociologists and psychologists, and The MLA Style Manual which is used in humanities. The Council of Science Editors and Vancouver styles are popular with scientists. Editors on Wikipedia may use any style they like, including styles they have made up themselves. It is unusual for Wikipedia articles to strictly adhere to a formally published academic style.
Isn't everyone required to use clickable footnotes like this[1] to cite sources in an article?
Yes. Footnotes (also called "<ref> tags") or shortened footnotes are now required in new articles, although some older articles may still use the now-deprecated citation system of inline parenthetical referencing (see WP:PARREF).
Why doesn't Wikipedia require everyone to use citation templates in every single article?
Citation templates have advantages and disadvantages. They provide machine-readable meta data and can be used by editors who don't know how to properly order and format a citation. However, they are intimidating and confusing to most new users, and, if more than a few dozen are used, they make the pages noticeably slower to load. Editors should use their best judgment to decide which format best suits each specific article.
Isn't there a rule that every single sentence requires an inline citation?
No. Wikipedia:Verifiability requires citations based on the content rather than the grammar. Sometimes, one sentence will require multiple inline citations. In other instances, a whole paragraph will not require any inline citations.
Aren't general references prohibited?
A general reference is a citation listed at the end of an article, without any system for linking it to a particular bit of material. In an article that contains more than a couple of sentences, it is more difficult to maintain text-source integrity without using inline citations, but general references can be useful and are not banned. However, they are not adequate if the material is one of four types of content requiring an inline citation. The article Early life of Joseph Smith, Jr. is an example of a featured article that uses some general references.
Can I cite a sign?
Yes, signs, including gravestones, that are displayed in public are considered publications. If the article is using citation templates, then use {{cite sign}}. You may also cite works of art, videos, music album liner notes, sheet music, interviews, recorded speeches, podcasts, television episodes, maps, public mailing lists, ship registers, and a wide variety of other things that are published and accessible to the public.