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

Yes, if what you determine the gain to be is correct, and regardless of any tax due.  If there is any income within the estate for the tax year that is  $600 or more, a Form 1041 must be filed.

Yes assuming the estate received the proceeds and then distributed the gain to them, each beneficiary needs the K-1 if there is income distributed to them.

The distributable net income may indicate there is no tax however if there truly was a gain, it will be distributed to the beneficiaries. 

You definitely have a stepped up basis due to inheritance, and it seems you understand that, however you also say there is a gain in excess of the filing requirement.  

• Form 1041 Instructions

So on Form 8949 ... describing the sale of the house which generated all the capital gains  ... is "date acquired" (Part II column b) the date he originally acquired the house  )from the point of view of the individual) or do I use his date of death (from the point of view of the estate)? 

You would use the date of death at the date acquired, as that is the day the trust acquired it. Any gain should be considered long term capital gain even if the property was not not held for more than a year by the estate.