DMed for the first time yesterday and one of the things I feel I need to sort out, among other comments, improvements, and similar, is how combat itself is actually initiated.
The main example I want to use involves instant actioning attempting to generate surprise conditions by players. Here the characters have entered a ruined city and generally been noisy about the whole thing - using a spell to make their voice louder and literally ask if there is anyone about. Any enemies around probably know what something is about to kick off but arguably don't know precisely what.
After resting the PCs head up a long flight of steps to a temple on the edge of the city. At the top only one crests and finds 3 bandits lounging around, chatting, and doing whatever bandits do in their spare time. After a brief exchange of pleasantries a combat starts:
DM "The bandit spits in your direction 'we're not done looting the temple, so you can clear off', and starts raising his crossbow as his mates emerge from their cover behind the pillars...
PC "I cast Firebolt at Bandit Keith"
DM "Hang on, I hadn't finished, everyone rolls for initiative...
Which sparked a debate about whether or not the PC could preemptively cast/attack before the combat starts by "instant actioning" (as above) as I was describing the start of the combat. As far as the bandits are concerned a lone half-elf who is pretty heavily armed has popped up in front of them, not even tried to be diplomatic, and ended up saying something rather suggestive about their mothers. The PC then asked about it being "surprise" because the bandits wouldn't necessarily expect an attack, but my view of "surprise" is closer to an ambush where one party is unaware of the other's existence.
(This precise example is close to how this question about standoffs works, however this specific PC was always the first of the party to go into rooms (only one with darkvision) and consistently felt they should get free rounds at the start of combat based on declaring attacks before I could "start" the combat.)
The second example the party came to more bandits, who were not alert immediately, in an underground room. They used magic to yell something obscene at the bandits and shut off all the torches so the bandits were effectively blinded. At this point they wanted to burst into the room casting spells, swinging maces, and playing some "meaty chords" (the bard's words, not mine). Again they wanted surprise arguing that, despite the fact that the bandits were yelling and cursing in confusion, they couldn't be sure they were actually being attacked as such. In the end a character with darkvision wanted to sneak in to a corner and again wanted surprise based on passing stealth rolls, so they would start the "combat" by firing a crossbow. At that point I think I relented because it was clear that they would do anything to try and win combats in a single round.
In a nutshell, my question is: "how liberally can the concept of surprise be applied to combat - is it only when one party is literally unaware of a threat (as I read the rules), or just when they are caught slightly off guard by the exact situation?"
NB I already plan to address the attempts at interrupting descriptions with actions next session, because it happened at other times and actually threw me off quite a bit.