The board insisted that she be present (C1 Grammar)

After formal verbs that ask for something to happen (suggest, recommend, insist, demand, require, propose, request, urge), the that-part uses the base verb for every subject — no -s, no is / are. So it is "that she be" and "that he submit", even with he / she / it. For a passive, use be + the past participle: "that the report be completed". Three versions are all in use: that he submit (the bare base verb, standard in American English and in academic writing everywhere), that he should submit (the usual formal choice in British English), and that he submits (everyday). All three are formal enough for a report; the bare base verb is the safest in academic writing. Watch out: with insist and suggest the base verb changes the meaning, not just the tone. "The board insisted that she be present" is a demand; "The board insisted that she was present" reports what they claimed.

After demand-and-recommend verbs: the base verb

It is essential that ... : the base verb again

After It is + essential / vital / crucial / important / necessary / imperative + that, the that-part again uses the base verb for every subject. The form signals a formal requirement, so use follow, not "follows", and be, not "is". Like the verb pattern, the bare base verb is the American and academic default, should + base verb ("that every participant should follow") is the common British formal choice, and the everyday follows turns up in more relaxed writing. Keep the bare base verb for formal, official writing.

The negative: that he not resign

To make the subjunctive negative, put not straight before the base verb — with no do / does / did. So it is "insisted that he not resign", never "that he doesn't resign". For a passive, it is not be + the past participle: "recommended that the clause not be included". The negative keeps exactly the same formal register as the positive subjunctive; a plainer alternative is should not ("that he should not resign").

Were for every subject in unreal situations

For an imagined or unreal situation, formal English uses were for every subject — I / he / she / it were. You will meet it after if, I wish, as if / as though, and would rather: "If I were", "I wish it were", "she acts as if she were in charge". Was ("if I was") is standard in speech and in plenty of writing, so treat this as a register choice rather than a right-and-wrong one: were is what formal writing and exams expect. Two places take were and nothing else: the fixed phrase if I were you, and the inverted form, where you drop if and put were first — "Were I in your position..." (you cannot say "Was I in your position").