"It was a hot night."
Translation:Byla to horká noc.
To byla horká noc. ? Could someone give me the main principles of the Czech word order?
As ortocymen says, the word order is made to emphasise something in the sentence. Here, "byla to horká noc" is a neutral statement, while "to byla horká noc" is something more along the lines of "man, that night was hot", implying that there was something exceptional about the night's hotness.
If you are just learning, I wouldn't really worry about these kind of subtleties. They are really hard to understand, and it is almost necessary to get a feel for them to use them correctly (I know, this is a hated statement, but I can't recommend otherwise).
Czech word order is loose to allow emphasizing certain parts of a sentence. It is very difficult to give you rules or common patterns (more so for me, a native speaker). As far as I understand you should not start a sentence with a predicate, but with subject, object or adverbial (of manner/place/time...)
In this case you can say with very slight difference in meaning all: Byla to horká noc. To byla horká noc. (Ta) noc byla horká.
No, the auxiliary verb is strictly not used in the third person. (And in archaic texts you would need to use the archaic form of je anyway and with a different word order...)