Give an unwilling holder a save and/or have the memory break when the holder takes damage
Rule #1 in Euch's personal Item-Creating Rules that He Just Now Made Up is:
Give the DM an out.
While weaponizing one of these orbs would be difficult, the reward would be instant victory over an encounter. I would hate for a final showdown with the main antagonist to somehow end after two rounds of cunning and trickery followed by poking a paralyzed dragon until it dies. I'm all for rewarding cunning and trickery, but epic-level creatures should be uncheesable. This item could cheese them.
Also, I would clarify (or be ready to clarify) the "when a spell is cast into" bit. I think what you mean is when the orb is the target of a spell. But with it's current wording you could argue that AoE spells that encompass a person holding one of these should have it triggered.
To directly answer the question: not game-breaking
I wouldn't use the words "game-breaking" to describe a Memory Orb, but would also say the item offers a perpetual, viable alternative to combat as a whole, which most players and DMs alike are going to find undesirable.
Geas itself doesn't say.
In principle the victim just has to understand the orders at the time they're given. However, if they don't remember being given orders, they may have no idea of what they have to do to satisfy the geas. That's a bad situation to be in.
One way to do what you describe would be for the NPC to have cast geas earlier, but not given any instructions yet. Then instead of speaking a trigger word, the traitor would just say "Protect me" and the geas would enforce the command.
Geas is not a great tool for this.
The problem is that the traitor needs the victim to cooperate for the duration of the fight, but geas will only zap them once per day. If the player decides to disobey, he will instantly take 5d10 damage, without warning. If he survives that, he's now completely free to disobey again, as much as he wants, with no fear of reprisal.
For this purpose I'd consider homebrewing a geas variant that lets the caster choose how much damage to inflict for each act of defiance, up to some cumulative maximum. This lets them fire some warning shots.
Discuss this with the player, privately.
One failure mode in this whole plan is that many players resent having this stuff sprung on them. Because they weren't prepared to betray the real people sitting at the table with them, they'll likely "fight" on behalf of the traitor as ineffectually as they can. In practice this means either that player sits on the sidelines during a protracted fight against the traitor, or the traitor gets curbstomped by the rest of the party, depending how tough you make the guy.
(Another issue is that geas applies a charm effect and the player needs to know they're charmed so they can act accordingly. Not telling them in advance greatly increases the risk that you'll have to tell them at the table and tip off the rest of the group.)
To have a PC with unreliable memories, you need some level of buy-in from the player. This doesn't have to mean giving away the twist, so long as the player knows there is a twist and is willing to go where it leads. You can say something like "I'm thinking that while you were away from the party, some things happened to your character that they don't remember, for reasons that will become clear later. Are you OK with that?"
Example. I had a PC who barely escaped an attack by werewolves, and got infected with lycanthropy, but didn't know it. I texted the player and said "Hey, your character is now a werewolf. In 2-3 sessions we're going to have a full moon, and you'll turn into a murderbeast." He thought this was pretty awesome, and when the time came he competely ran with it.
Best Answer
Probably No
You can certainly give the target a dream in which they relive things that happened in the past months. You probably cannot have them relive three months' subjective experience in ten minutes, but that's up to your DM.
You can probably convince your target that a dream was real. The spell doesn't explicitly say you can do this, but it seems in line with other things the spell allows. Your DM will probably allow this.
But your modify memory spell will only let you affect the version of the events that your target has just experienced. The original memories will remain intact. So now your target thinks: "Okay, I went to the castle a month ago and I saw a creepy wizard looting the treasury. But then I also went to the castle five minutes ago and I saw a goblin looting the treasury and the creepy wizard was trying to prevent it. Also, how did I get back from the castle treasury to my bed in the span of five minutes? That's weird."
The modify memory spell notes that weird inconsistent memories may be ignored by the target, and I think that's likely to happen here.
It's not clear how the dream spell is helping you here. If you want the target to think they went to the castle, you can just tell them that using modify memory; there's no need to make them dream it first.
If you upcast the modify memory spell, you can affect the target's original memories without bothering with dream.