Depois que o contrato for assinado, a mudança pode começar.

Depois que introduces a clause with a verb (a full action/event): Depois que o contrato for assinado = after the contract is signed.
Depois de is normally followed by a noun or an infinitive:

• Depois de assinar o contrato, ... = after signing the contract
• Depois do contrato, ... = after the contract (less specific)

for assinado is future subjunctive of ser (for) + past participle (assinado) in a passive construction.
Portuguese typically uses the subjunctive after time expressions like depois que, quando, assim que when the event is in the future or not yet completed.
So it’s “after the contract is signed (in the future)” → Depois que ... for assinado.
será assinado (future indicative) is grammatically possible in some contexts, but it often sounds more like a firm prediction/statement and is less common after depois que than the subjunctive in everyday Brazilian Portuguese.

It’s an irregular form. The future subjunctive of ser is:

• quando eu for
• quando você/ele for
• quando nós formos
• quando vocês/eles forem

So o contrato for assinado literally uses ser in the subjunctive: “that the contract be signed.”

Yes. ser + participle = passive voice: ser assinado = to be signed.
This sentence doesn’t mention the agent (the signer), which is very common when it’s not important or is obvious from context. If you wanted to include it, you could add por:

• Depois que o contrato for assinado pela empresa, ...

In the passive voice, the past participle agrees with the subject of the passive clause. Here, the subject is o contrato (masculine singular), so the participle is assinado.
If it were a proposta, you’d get: Depois que a proposta for assinada...

Yes, and it’s common. estar + participle focuses more on the resulting state (“once it is signed / once it’s signed and done”):

• Depois que o contrato estiver assinado, ...
  ser + participle focuses more on the event/process (“after it gets signed”).

Because the sentence starts with an introductory dependent clause (Depois que...). In Portuguese, it’s standard to separate that introductory clause from the main clause with a comma:

• Depois que X, Y.

mudança can mean both change and a move/relocation. In a context with contracts, it often means a relocation (e.g., moving house or moving offices), but the sentence alone allows either meaning. The rest of the text usually makes it clear.

pode (from poder) expresses possibility/permission/feasibility depending on context:

• “the move/change can start” (it becomes possible)
• “the move/change may start” (it becomes allowed)
  It’s less absolute than vai começar (“will start”).

After modal verbs like poder, the next verb usually stays in the infinitive:

• pode começar = “can start”
  You don’t conjugate começar there because pode already carries the tense/person.

Often, yes, with slightly different nuance:

• Quando o contrato for assinado... = “when the contract is signed...” (neutral timing)
• Assim que o contrato for assinado... = “as soon as the contract is signed...” (immediacy)
• Depois que o contrato for assinado... = “after the contract is signed...” (sequence emphasized)