1. Yes. Its the most sensitive work for a MM consultant. The main caution is that, if you open a posting period, its not a easy job to re-open the previous period (You may have to contact SAP for that).
2. Right. the period is not stored anywhere in table. Only posting date is stored in various table.
3. See, SAP allows only 2 months for posting a Material document number.
Normally When you open a period from MMPV, then the current period will open.
Now if you missed some to post a document in previous month, then SAP has given the option, that you can only post on previous month.
Now as per your requirement.
If you open the period July, then you can only post any document in July and previous month as June.
You will never can't able to post any document in month May.
As it is not 6th June, in meantime, if your organization want to post a document in May, then what can you do?
You can do nothing because you can reopen the month May. Forcefully you have top post the document in June month.
To avoid this, I have said take a proper document to open posting period in advance. It will be much better for you.