Yeah, but as Sasha himself said those guards chasing Hayu were way out of town which is not normal, and unlikely to be for any totally legit purpose. And on top of that y'all killed one of their own.
It's not going to be guards coming to make an arrest and put the offenders on trial, they're not going to care about "self-defence".
It's also not about getting through town, it's about said guards and elven assassins not being able to pick random townsfolk and say "You seen a beardless dwarf, a goblin, another dwarf and some humans who look like [discription]" and have the reply be "Oh that lot, weird bunch they were. Saw them down the docks talking to Dishonest Al about hiring a ship." Then trundling over to the docks and asking where we went. Rinse and repeat until they catch up to us.
The elves at least, being the campaign bad-guys, are going to find us at somepoint because GM. But there's no point in making it easy.
As for the horse that where the people with the good lying skills do something like this;
Liar one "Hey stablemaster, I found this horse with a brand wandering around about yay-far out of town*, wounded and all saddled up, and am turning it in like a good citizen."
Liar two " I just happened to be passing by, completely unrelated to Liar one there, and overheard you talking about a branded horse. Let's have a look, whoa I recognise that mark. Those people offer a reward for their missing horses, especially if they turn up fully saddled minus the rider. I'm heading to [place that groups from] anyway, I'll give you [twice horse value] as your share of the reward I'll get when I take it in, Liar one."
L1 "Sweet, but can you make it quick I have to leave immediately for reasons" L2 "Shit, I don't have enough on me. Stay right there while I go get the rest from my friend/room I just checked into/other" runs off.
L1 "Look stablemaster, I really, really need to go. How about you give me [1.5x horse value], I'll leave it with you and you'll make an easy [.5 horse value].
Hamster wheel turns in stablemaster's head L2 was really quick to offer [2x horse value] I could totally negotiate for even more money.
Stablemaster " Sure." -- impatient sucker, can't even haggle----
- Yay-far being somewhere around where the fight with the guards took place