Do I need to file 1041 if no tax is due?

Sold father's personal residence during probate, all proceeds distributed to beneficiaries. We got a late 1099-S form for the sale, and due to stepped-up basis there's only about 5K in long term gains. There was no other income and no tax seems to be due. 

1. Do I still need to file the return, even if calculations show no tax due?

2. Do I need to send K-1 forms to beneficiaries even if the distribution isn't taxable? 

 

One IRS publication said we need to file if we get a 1099-S, which makes me think I need to file even if no tax is due, but I'm not sure what to do about K-1s.

 

Thanks in advance