Is it correct to say: "All praise is due to Allah alone, and all thanks are due to Him alone"?

There is no objection to praising Allah with "Alhamdulillah, a great, pure, blessed praise" and similar phrases. The forms of praising Allah are not restricted to what is authentically transmitted (ma'thur). It has been reported that twelve angels rushed to raise these words when a man uttered them during prayer. It is permissible to introduce a non-transmitted form of remembrance (dhikr) in prayer, as long as it does not contradict what is authentically transmitted.