One comment regarding स्ते - Devnagri consonants can be divided in two groups: those that contain the "pāī" (the vertical stroke symbolizing the intrinsic "a") and those that don't. The examples of the first group are: म ल व स etc. The second group includes ट ठ and so on. When you want to suppress the "a" in consonants of the first group you drop the "pāī" and stick the rest the next consonant (or else it would fall without the leg ); the halant is not needed - this is how स्ते is formed. The halant is used to remove the "a" from the second group of consonants (because they do not have the stroke that could be removed) and only when your typesetting tool does not allow the fancier ligatures as shown in the table quoted by @FurbyZeKat .
The next complication to "ST" is "STR" like in the word for Australia: ऑस्ट्रेलिया
That "^" under the "ट" in स्ट्रे consists of two strokes: the one going from top to bottom right is the halant that removes the "a" from behind the "ट", the other stroke going from the top to the bottom left adds an "r" after that. Isn't that challenging?
I am not 100% sure whether what I write is correct; if not I hope that someone with better knowledge corrects that...