I am not a lawyer. But this is what I recommend for the parts besides the explanation of the state of the marriage. For that, I agree that you should seek advice of how best to decribe what happened.
Collect all the documents that the immigration authorities are asking from you, and send them in before the deadline they have set you.
Proof of Employment
Collect this for your current job as well as for all previous employment you have had, Switzerland.
If you do not have a written contract, then ask your employer(s) to provide one. In case they won't or won't do it right away, then you prepare the outline as a draft. That way, you save your employer the work and help them to get you the written contract faster. List your full name, date of birth, address, AHV-Number (it is usually shown on the back of your medical insurance card), the date on which you commenced work and write up a brief job description and conditions of work and remuneration, and give it to the employer to use as a start.
If there is any employer for whom you cannot get a written contract, you can also prove your employment with your bank statements. For your own privacy, cover up other transactions.
Another way to do it is to request a statement of your social security contributions from your local SVA office, to which each employer must have paid your contributions.
Proof of Rental
As you do not have the rental agreement, ask your landlord to send you a copy. If they ask you why, simply tell them you can't find the original, that's all you need to say. Such a copy should, ordinarily, not be a problem to get.
If - because as you say your partner had been dealing with all those matters - you do not know who the landlord is, then have a look in the entrance of the building where there is often some sort of sign with the contact numbers of the landlord or the caretaker, or else ask your neighbours for the contact details of the landlord.
Proof of Language
As you will not have the language certificate before the deadline the immigration authorities have set, at least send in the proof that you have registered for an test, proof of your payment of the fees, and a print-out from the test centre's info showing that the result will be available in 4 to 8 weeks. Calculate those actual anticipated dates, write them in your covering letter that and add that you will submit the test results to the immigration department as soon as you have them.