Putting aside the logic of marrying someone you have only been with for a few days I think even Manilla might find this a stretch.
Why do you not want to spend time together?
Presumably Ireland?
Not sure how many here are familiar with Irish Criminal Law, from a practical perspective the decision will be made at the interview, if a waiver is needed.
The K1 has many disadvantages but not in relation to this.
A 12 year old should be looking at a B2.
Let her parents apply for the visa and yes you will need their permission for you to travel with her without them.
Get married in Mexico?
Visiting the other half can cause issues when applying for a visa, hopefully she did disclose you.
She can always apply for a new visa.