Si la manejas con descuido, podrías quebrar toda la vajilla y perder mucho dinero.

In Spanish, after si meaning if (a real or possible condition), you normally use the indicative, not the subjunctive: Si la manejas...
The subjunctive after si is used in different patterns (like Si la manejaras...), which expresses a more hypothetical or less likely situation.

In Latin American Spanish, manejar can mean to drive, but it can also mean to handle / operate / manage something (a tool, a machine, a fragile object, etc.).
Here it means to handle it (because the next part talks about breaking dishes).

La is a direct object pronoun meaning it (referring to a feminine noun, like la caja, la bandeja, la vajilla, etc.).
In front of a conjugated verb, Spanish places object pronouns before the verb: la manejas = you handle it.

Manejas is the tú form (informal you). If you wanted the formal usted, it would be:
Si la maneja con descuido, podría...
The rest of the sentence would adjust accordingly (podría instead of podrías).

Podrías (conditional) expresses possibility in a more hypothetical/softer way: you could break everything.
Puedes (present) is more direct: you can / you’re able to. It can sound like ability or permission, not just risk.
So podrías fits the idea of a potential negative consequence.

Si + present indicative + conditional often expresses a realistic possibility and its possible result:
If you do X (now/in general), you could/would do Y.
Example pattern: Si comes mucho, te sentirías mal = If you eat a lot, you could/would feel sick.

Quebrar here means to break (especially something that cracks/shatters, like ceramics or glass). It’s common in many Latin American countries.
A very common alternative is romper: podrías romper toda la vajilla.

Yes. Quebrar can also mean to go bankrupt (for a business/person), depending on context.
In this sentence, the direct object toda la vajilla makes it clear it means to break physical objects.

La vajilla is a collective noun meaning dinnerware / dishware (the set of plates, cups, etc.). Even though it includes many pieces, it’s treated as singular: toda la vajilla.
You could say todas las piezas de la vajilla if you want to emphasize individual pieces.

Yes—y links a second consequence with the same subject (tú). The idea is:
If you handle it carelessly, you might break all the dishware and (as a result) lose a lot of money (replacing it, paying for damages, etc.).