Is the Texas Constitution older than the Constitution of the US?

Answer 1

No.

The Declaration of Independence signed in 1776 states in its last paragraph (bolding added by me for emphasis):

We, therefore, the Representatives of the united States of America, in General Congress, Assembled, appealing to the Supreme Judge of the world for the rectitude of our intentions, do, in the Name, and by Authority of the good People of these Colonies, solemnly publish and declare, That these united Colonies are, and of Right ought to be Free and Independent States, that they are Absolved from all Allegiance to the British Crown, and that all political connection between them and the State of Great Britain, is and ought to be totally dissolved; and that as Free and Independent States, they have full Power to levy War, conclude Peace, contract Alliances, establish Commerce, and to do all other Acts and Things which Independent States may of right do. - And for the support of this Declaration, with a firm reliance on the protection of Divine Providence, we mutually pledge to each other our Lives, our Fortunes, and our sacred Honor. The United States Constitution was adopted on September 17, 1787 and ratified by the 13 states at the time. The Constitution was ratified by the approval of nine states, with New Hampshire being the ninth state to ratify (or approve) the Constitution on June 21, 1788. The Federal government as we know it today started operation on March 4, 1789. When the Federal government started, only Rhode Island and North Carolina has not ratified the Constitution. Rhode Island was the last state of the 13 original colonies to ratify the Constitution in 1790, and it passed by just two votes, 34 for, 32 against.