The male voice and female voice seem to pronounce this differently. Specifically the male clearly enunciates the T in ecrit. Is this just natural variation in speech or is there something else going on? Thanks!
It's a natural variation. The male voice has an accent typical of what you would hear in the southwest of France. It is normal.
Since the root word is Ecrire and it ends in -re does that mean that the je and tu conjugations would end in -s and not -t?
Starting with je, it would be, "J'écris, Tu écris, and then Il écrit." Respectively, it is, "I write, you write, and then he writes."