Learn Hardcore Japanese: ibento no sankasya zenin de kankyouhogo no mokuhyou wo kyouyuusimasita. - All the participants shared their environmental protection goals.

イベントの参加者 = “participants of the event” (イベント modifies 参加者)
環境保護の目標 = “goals for environmental protection” (環境保護 modifies 目標)
This usage is similar to English “X’s Y” or “Y of X,” not a literal “of” but a general attributive connector.

Why is there a で after 全員? What’s the difference between 全員で and 全員が?

全員が simply marks “everyone” as the subject of a verb (“everyone did X”).
全員で indicates that the action was carried out collectively by all members: “with everyone” or “as a group.”
In our sentence, イベントの参加者全員で emphasizes that all the event participants took part together in sharing the goals.

Why is there no explicit subject in this sentence? Who performed the action?

Japanese often omits the subject when it’s clear from context. Here, ～で on 参加者全員 makes it clear that the participants themselves performed the action. There’s no need to repeat “they” or “we”; the listener infers it.

What nuance does 共有しました carry compared to verbs like 伝えました or 発表しました?

共有する implies mutual distribution and joint understanding – everyone ends up “holding” the same information or goal.
伝える is one-way: you convey information to someone.
発表する is formal announcement, often to an audience.
Use 共有しました when you want to stress that all parties came to share and agree on something together.

Can I say イベントの参加者全員に環境保護の目標を共有しました to mean “we shared the goals with all participants”?

No. Because 共有する is by nature mutual, you don’t mark recipients with に. If you said ～に共有しました, it sounds like one-way delivery rather than mutual sharing. To express “we shared with the participants,” you can say:

私たちはイベントの参加者全員と環境保護の目標を共有しました
or use a one-way verb like 伝えました if you mean just “informed them.”

Are there alternative verbs for “share” such as シェアする or 分かち合う? How do they differ?

シェアする is a casual loanword, common in everyday conversation or tech/business contexts.
分かち合う is more emotional or interpersonal – “to share feelings, joy, sorrow.”
共有する is formal/businesslike and stresses equal access or joint ownership of information/thoughts.
Choose based on tone and context.

Could I shorten イベントの参加者 to イベント参加者? When is omitting の acceptable?

In formal writing or compound-noun headlines, dropping の (イベント参加者) is possible as a tighter compound. In spoken or everyday text, イベントの参加者 is clearer and more natural.

How would I express this sentence in a more casual style?

Switch to the plain past form and/or use a more conversational verb:

イベントの参加者全員で環境保護の目標を共有した。
Or even more casually: イベントのみんなで環境保護の目標をシェアしたよ。