With a year end of May 31st you must be dealing with a corporation rather than a proprietorship.
I am not an expert on Entrepreneur but from a number of postings on this site suspect that it may be to simple a program for a corporation, you might want to consider an upgrade.
Now to your specific questions:
1) You can't enter transactions beyond the YE until you advance to the new year. You might want to save a copy under a new name and advance that copy to the new year.
2) You need to speak to your accountant about what programs s/he works with. You might find that Simply Entrepreneur works just fine, or you might need to export into a format this person works with.
3) When you advance to the new year Simply will close all the income and expense accounts to Retained Earnings.
By the way, you have not given your accountant much time to perform his or her due dilegence, prepare your financial statements and tax return. Just a thought for next year