[AngelicaDeAlquezar]

Originally Posted by ChicadeJeep

Okay - I have redone again: Newest in purple.

¡Es lamentable que no le haya dijo a su familia! (I think that all I had to do was add the haya in?)

Ahora la familia cree que Carlos les ha engañado a todos.
¡Es no es cierto que haya engañó a su familia! (I think that all I had to do was add the haya in?)

Wrong in both cases. "Dijo" and "engañó" are simple past, and both because of the exercise reasons and the sentence structure, you have to use a subjunctive:
-> Es lamentable que no le haya dicho a su familia.
-> No es cierto que haya engañado a su familia.
"Haber" is an auxiliary verb used for conjugating composite tenses. It needs a past participle.

If you still haven't learnt those tenses, you can follow one of Chileno's previous suggestions and make the sentences with subjunctive preterite:
-> Es lamentable que no le dijera a su familia.
-> No es cierto que engañara a su familia.

Originally Posted by ChicadeJeep

Probablemente Arturo vendrá a México a reunirse con Raquel.
¡Espero que ella sea feliz! (I changed it to I hope she will be happy - does this work better?)

You could also have kept contento(a): "¡Espero que ella esté contenta!"