could this work?
No. All weapons with the "heavy" property have the two-handed property as well. Here's exactly what each property does (PHB 147):
Heavy. Small creatures have disadvantage on attack rolls with heavy weapons. A heavy weapon's size and bulk make it too large for a Small creature to use effectively.
Two-Handed. This weapon requires two hands when you attack with it.
The heavy property itself isn't a problem here, but the two-handed is. Since all heavy weapons are also two-handed, you must use two hands to wield them. The enlarge spell doesn't give you the ability to wield a two-handed weapon in one hand, even if that weapon wasn't enlarged with you. Your DM might allow it, but it's certainly not part of the Rules As Written.
So what can you dual wield, then? Here's the rules on two-weapon fighting (PHB 195):
When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in one hand. You don't add your ability modifier to the damage of the bonus attack, unless that modifier is negative.
Based on this, you can only dual wield light melee weapons. You don't even need the two-weapon fighting style, since all the fighting style does is allow you to add your ability modifier to the bonus action attack. There is a way to get around the "light" limitation, namely the Dual Wielder feat (PHB 165, emphasis mine):
You master fighting with two weapons, gaining the following benefits:
- You gain a +1 bonus to AC while you are wielding a separate melee weapon in each hand
- You can use two-weapon fighting even when the one-handed melee weapons aren't light
- You can draw or stow two one-handed weapons when you would normally only be able to draw or stow only one.
This feat allows you (among other things) to use any one-handed melee weapons for two-weapon fighting.
In conclusion, you're not going to be two-weapon fighting using greatswords, even if you're enlarged. The closest you're going to get would be two longswords with the Dual Wielder feat
Side note: If you want to do two-weapon fighting purely from an optimisation perspective, you may want to reconsider. It is generally accepted as one of the weaker playstyles, as it uses your bonus action to be effective (needed to cast smite spells on a paladin, for example), and still can't quite compete with great weapon fighting, especially if you factor in the Great Weapon Master feat. It doesn't fall completely behind other playstyles, so if you want to do it because of a character concept, go ahead. But if it's exclusively for optimisation, it might be better to just use a single greatsword.
It's up to DM. Yes, it's a plain, old, simply, boring answer but there is no RAW with which to rule by.
The eldritch knight's weapon bond simply states that you bond with a weapon and can summon that weapon to you. It doesn't say anything about what happens if the weapon is broken and it's likely something the designers either didn't think of or purposefully didn't make a ruling for in order to not bog the game down with rules for every little thing. It's also not stated what breaks that bond, aside from breaking it to bond with a third weapon.
As such it's left up to the DM. If the plot requires you to trek halfway across the world to retrieve the weapon then you can be sure that's what you'll be doing instead of being allowed to summon it back. If the DM decides that a broken weapon also means a broken bond then that's their prerogative. It's not like it's anything particularly game breaking to allow a broken weapon to be summoned but it could reasonably depend on how broken it is and what the weapon is (mundane as opposed to magical or powerful artefact). Two pieces, sure they could allow it; shattered into a thousand pieces, what's the point.
Best Answer
Seems like surprise is the tool for the job
The rules don't allow it directly, but you're spending resources to do some scouting, which is clever! You should be rewarded for playing cleverly!
I think if a player tried to do that at my table, I'd handle it like this: Make the player attack the wall (see below; if I can't remember it off the top of my head, I'd probably just make something reasonable up on the spot to save time).
This will roughly do what you want to do, but all within the framework of the rules, so try and pitch this to your GM and work with them to find a solution that works for both of you. I hope you find a way to make it work!
Response to a hypothetical objection:
"But Pierre, what if the players start doing that all the time and cheesing every encounter with surprise?"
Dear GM, consider yourself lucky. Your players are using every tool at their disposal and taking time to scout fights beforehand. They're bringing their best game and are spending time and resources coming up with clever and cinematic ideas. Don't punish them for it!
On AC and HP for walls:
DMG p. 246-247 gives tables for object AC/HP depending on material, size and sturdiness. Using those tables, a stone wall (large stone object) could have an AC of 17 and HP anywhere between 5 (fragile wall, old/misshapen stones, crumbling mortar...) and 27 (resilient wall, well-cut stones, expertly adjusted good quality mortar).
This section of the rules also mentions resistances and damage thresholds, which could both apply to this case; I recommend you read it.