How did the u. s constitution and the bill of rights address the grievences expressed earlier in the declaration of independence?

Protection against those grievances were included in the Constitution and the Bill of Rights, to protect US citizens from such things in the country they were establishing.

I'll offer just one example as a case in point:

Quartering of soldiers meant soldiers would have the right to enter your home and expect you to provide them food and lodging.  That was seen by the colonists as invasive of their personal rights, and was raised as a grievance in the Declaration of Independence.

The issue of quartering of soldiers appeared not only as a complaint in the Declaration of Independence, but also became a featured right in the Bill of Rights of the Constitution.  The 3rd Amendment states:  "No Soldier shall, in time of peace be quartered in any house, without the consent of the Owner, nor in time of war, but in a manner to be prescribed by law."

a historian researching the immigration policies of the early 1900s would expect a source written today,rather than in 1910 to :

( a ) be more interested in objective data and statistics.