My spouse passed away in June. We had filed jointly in the past. We had been using Self Employed TT She had a small amount of income in 2018. What now?

You can still file your 2018 return as Married Filing Joint,  and include her income.  Starting next year, you'll have to file as Single, or, if you qualify, as Head of Household.

Do I have to indicate anywhere in TT that she is deceased?

Yes.  When you enter her name in the My Info or Personal Info section, you'll be asked if she passed away during 2018.

Thanks.  Also The children receive SSI benefits due to her passing.  From what I understand, that is not taxable as it is their only source of income, and is under their SS numbers.  Do I understand correctly?

That is correct.