It certainly will!
Also, the scene I just started positng right now broke my heart, but I'm an overly-emotional comics-auntie about my own characters, so I suspect I might have overreacted when I drew it. ^_^;
All the time, and not just with the heartbreaking scenes! I doubt myself a lot while I work on my comics - I think it goes with the territory, and isn't something you ever get entirely rid of. Doubting yourself to a certain degree can be good for your comic, because it makes you question stuff and really think about how and why you're doing stuff.
Avoiding clichés is something that gets easier if you read and watch a lot of other people's stories; you start recognising patterns and tropes and clichéd scenes, etc. Some stuff is cliché because it works - and there's no shame in using clichés, as long as you invest a bit of effort and actual feeling into it. The reason why One Piece manages to make me cry isn't because it is narratively original - it's stuffed to the gills with shounen anime tropes - but because it wears its heart on its sleeve and isn't afraid of genuine emotions being invested in those clichés.
Most of my heartbreakers are going to happen later on in the story (unless you count the current scene, which as I said, might only be heartbreaking to me), after the readers have spent a LOT of time getting to know the characters and become invested in them. It's hard to break someone's heart on page one, because at that point, they have no idea who these people are and why they should care. It's easier to break someone's heart by page 100, because by then they know why they should care.
It also helps to build up either a sense of inevitable doom - as in, your characters can't avoid this no matter how hard they struggle - or one where a character's choice is instrumental in changing the outcome of a situation. Say, someone choosing to sacrifice themselves to save their friends - that's heartbreaking, but it's an active choice by the character, rather than a random act. It's something they could have chosen not to do, but they did.