Is it allowed to :-
To say Alhamdulillah or La hawla wa La Quwaata illa biLlah or any rememberance and glorification of Allah in sujood while praying.
Yes it is allowed to do some dhikr and thanking Allah while prostrating as long as it is not to excessive. It is even recommended to perform dua' while prostrating:
The Messenger of Allah (ﷺ) said: The nearest a servant comes to his Lord is when he is prostrating himself, so make supplication (in this state). (Sahih Muslim)
... So far as Ruk'u is concerned, extol in it the Great and Glorious Lord, and while prostrating yourselves be earnest in supplication, for it is fitting that your supplications should be answered. (Sahih Muslim)
I asked 'Ata': What do you recite when you are in a state of bowing (in prayer)? He said:" Hallowed be Thou, and with Thy praise, there is no god but Thou." Son of Abd Mulaika narrated to me on the anthority of 'A'isha (who reported): I missed one night the Messenger of Allah (ﷺ) (from his bed). I thought that he might have gone to one of his other wives. I searched for him and then came back and (found him) in a state of bowing, or prostration, saying: Hallowed be Thou and with Thy praise; there is no god but Thou. I said: With my father mayest thou be ransomed and with my mother. I was thinking of (another) affair, whereas you are (occupied) in another one. (Sahih Muslim)
The guiding line should be to pray as the prophet () used to pray and therefore we shouldn't forget to use supplications and dhikr he used to use. Here some examples:
... And when he prostrated he said: "Subahana Rabbial-A'la, Subahna Rabbial-A'la (Glory be to my Lord Most High, glory be to my Lord Most High)." And between the two prostrations he would say: "Rabbighfirli, Rabbighfirli (Lord forgive me, Lord forgive me)." (Jami' at-Tirmidhi, Sunan an-Nasa-i, sunan abi Dawod and sunan ibn Majah)