This proposal is very helpful because I can only speak English using the google translation.
If native speakers tell me grammar mistakes in this thread, I will correct them.

Thanks. I corrected it.

Still wrong, it should be : " Spend political power to make X into a core state " where X = the name of state. Sorry if I confused you above

I'm playing some now that the mods I use are all updated. Will examine text as I go.

@Micteca Hello :) I have some translation changes to suggest. I have looked at how Paradox writes their information and tried to write in a similar way. All grammar is exactly as intended.

These suggestions are listed as your text, then my change.

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[Tool Tip]
Make Core
Spend political power to make “name” state a core.

[Changes]
Gain core on state
Spend political power to integrate “name” as a core state.

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[Action Window]
Make Core
Do you wish to make “name” into a Core state?
The cost of make “name” into a Core state is “##”
.
It would take “###” days.

[Changes]
Gain core on state
Confirm?
It costs “##” to integrate “name” as a core state.
-
Time to complete: “###” days

+++++++++++++++++++++++++++++++++++++++++++++

[Tool Top after Action]
We are currently working on making “name” a core.

[Changes]
“Name” is currently being integrated.

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[Action Button]
Fabricate Claim
Fabricate a claim on a state.

[Changes]
Fabricate Claim
Forge a claim of core status on this state.

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[Tool Tip]
Justify Power
Power change: -1.00 per day.
Base value: -1.00
--------------
Justify Power represents the ability to justify claims by forgery of documents or propaganda, which we have for this state owner.

[Changes]
Justify Power
Power change: -1.00 per day
Base value: -1.00
--------------
Represents your influence (via propaganda or legal tampering) over a country you are justifying war against. It costs Justify Power to forge claims of core status on the states of that country.
- Justify Power decays after the states are occupied
- This provides benefits during the peace conference and post-war

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[Action Window]
Fabricate Claim
Do you wish to fabricate claim on “name”?
Fabricate claim will consume “##” to claim “name”.
The claim will make selected states cheaper to pick at the peace conference and lower the cost of making a core state.

[Changes]
Fabricate Claim
Confirm?
It costs “##” to forge a claim on “name”.
This will make “name” cheaper to select during the peace conference. Post-war the cost to gain “name” as a core state will be also be reduced.

+++++++++++++++++++++++++++++++++++++++++++++

[Confirmation Window]
Claims Fabricated
“Your Country” gained a claim on “name”.

They will invade “Target Country” to get “name” in the near future.

[Changes]
Claims Fabricated
“Your Country” gained a claim on “name”.

“Target Country” should prepare itself for the coming war.

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Hopefully this will help. If anything is unclear please ask. I also tried to keep some of the flavour and spirit you wanted. While being as clear and practical as possible for the players.

I edited the above based on a misinterpretation of a mechanic. Should be more accurate now.

Nice job fox

Sorry I'm late.
All corrected as per your proposal. Please let me know if there is a problem.

I forgot to reply. After playing, everything looks good.