First of all...
...cool idea for a spell. It's an interesting expansion for the game's magic tool set. But there are some issues:
Items with Self-Awareness
That's not directly a balancing issue, but there are many open questions.
If you can talk to items and the items can answer your questions... Can they lie? Can they lure you into an ambush? Are they loyal to their former owner? Can they decide whether to tell the truth or a lie? And if, how do you determine that? Is an item influenced by a Zone of Truth for example?
Or is it more like you can sense the surroundings of the item during the last X hours/days/whatever?
In that case, I'd recommend to solve it like described in Find Familiar
While your familiar is within 100 feet of you, you can communicate with it telepathically. Additionally, as an action, you can see through your familiar's eyes and hear what it hears until the start of your next turn, gaining the benefits of any special senses that the familiar has. During this time, you are deaf and blind with regard to your own senses.
Wich is better depends on your campaign-setting. If in your campaign setting all objects have a consciousness go with it. It can be a cool asset. But if objects in your setting work like in every other setting, don't ask questions your campaign setting doesn't answer itself. Don't answer those questions (regarding objects' self-awareness) through a spell.
The Spell's Cost
That's dang pricey. 100gp per question is way to high. Compare it to Divination (4th level Cleric spell).
incense and a sacrificial offering appropriate to your religion, together worth at least 25 gp, which the spell consumes
Where Divination asks for a single event that will happen up to 7 days in the future, your spell asks for a single event in the past of the touched item. So they should be comparable. Hence: 25gp instead of 100gp.
Further there are no spell costs that rise with spell increments. So give it a flat cost and ask about a particular event or time frame within the last 7 days. Again, compare it to Divination (again the spell not the school).
At many points it works like the opposite of your spell. So can compare the power level.
I know, I get nitpicky... but right now, your spell needs a tongue (that can be substituted through a spell focus) and 100gp per question, that the spell doesn't consume. So if you want to ask 4 questions you had to have 400gp in your wallet for example. I doubt this is intentional.
Is it balanced?
Besides the mentioned issues... yes, I think it's okay for a 4th level spell, because it's somewhat on par with Divination that is also a 4th level divination spell. Just lower the costs to a flat 25gp and think about the questions I asked regarding the item's self-awareness.
If you want conscious items, go for it... in that case I think 3rd level could be okay, too. Because if there's the possibility that an object can tell you fairy tales, it's a major decrement you can account through a lower spell level.
As promised in the comments
Speak with Object
3rd Level Divination
Casting Time: 1 Action
Components: V,S,M (a tongue of an intelligent creature and incenses worth 25gp, which the spell consumes)
Duration: 10 minutes
For the duration of this spell you imbue a touched object with a temporary consciousness. It gains the ability to understand and speak one language the caster is able to comprehend and that can be heard in a 30ft radius.
If not determined hidden by the DM the object is neutral towards the caster. For the duration of that spell, you can ask the item up to five questions (like in Speak with Dead). Depending on how the object's personality stands towards the caster it can answer a question truthfully or tell a lie. It can only answer questions about things that happened in their closest surroundings during their lifetime. For example: The names of former owners, the location and time of its creation or where it was stored, the name of its creator, information about other items that the object was stored next to, specific information that was talked about while the object was around, if the object spoke to someone through this spell in the past etc.
Questions the object doesn't know result in useless information or a lie but count against the maximum number of five questions.
Classes: Bard, Artificer, Wizard, Sorcerer
(Disclaimer: I'm not a native English speaker... so, sorry for wrong grammar or strange sentences... you maybe have to tweak it a bit)