Pretty sure, yes. Needed the TM.30 at all my extensions in different offices. You can obtain this in the very immigration office though - given the hotel has reported you there before - which they are required to do by law. Double check with your hotel that they did.
Varies, depending on the requirements of your immigration office. Unfortunately they have highly inconsistent requirements across the country. As a minimum, you will need your passport and a TM.30 receipt. Plus some forms filled out - which you get at the immigration office. Some offices might ask you for additional documents, like a letter / email from your embassy. Best to check with your particular office before.
Nobody knows for sure at this point. Although it is likely to be extended. If so, probably last minute on short notice, as it has been before. The rest of your question would seem to consist of a logical error, cause if it is NOT extended, no need to bring documents to immigration 😉
Only the first one. Subsequent COVID-60 extensions tend to be counted from the end date of the current COVID-60. Doesn't make much sense - but what does.
Depends. When you are coming directly from your original visa / entry stamp (i.e. if it is your first COVID-60 extension), they are counting from the day of application (so you may loose days if you go there early). If already on a COVID-60 day extension, the next extension will be added to the end date of the current one (so you will not loose days, if you go early). This is the general rule. Then again, TIT, nothing is applied coherently among different offices of the same organization, unfortunately.
Traditionally, extension of the COVID extension program has been announced last minute only. Either on the last day - or even retroactively a couple of days after it ran out before. Unfortunately.
Unlikely any immigration office will give you another extension at this point with you having more than 30 days left until May 1st. So I guess you can just hope they will be extending those 60-day extensions beyond March 30 - which I think is highly likely.