Mapping out my ancestry. Related to US Presidents & High Kings of Ireland?

I recently bought my grandfather an AncestryDNA kit. He believes that he shares a common ancestor or perhaps is a descendent from the 18th President of the United States, Ulysses S. Grant. He shares the surname and has been told by his relatives that are long dead that there is a connection on his fathers side to the president(The man pictured below). On his mothers side he believes that he is directly related to President Kennedys right hand man.

I may also be related to Tairrdelbach Ua Conchobair on my fathers side, who was a high king in Ireland during the 12th century.

My research has taken me as far back as 1847 so far. I have identified an Owen Grant of Carnaney who died in 1847, It looks like his son James Grant moved to New York and had put on quite the extravagant funeral for his father, costing 3 pounds 1 shilling and 5 pence, about £2000 in todays money(can be seen in the church record below). The real question is who are the two people named murphy buried in Owen Grant's grave over 100 years later with no explanation?

Either the year on the headstone or the date in the church books is incorrect, these kind of errors are not uncommon, especially dating back such a long time.

My grandfather was also able to show me the grave of his grandfather, he never knew the man but was interested to find out more. After doing some digging I found his baptism record from way back in 1874, as a result of this I found his father and mothers names. I know the name of my Great great great grandfather, how cool is that?!

In this volume of the text you can see that the priest has added in that Bernard had married Mary Murphy in 1911, which confirmed my grandfathers inclination of the Murphy connection.

That's all I have uncovered so far, I hope you found this interesting because I certainly did!