Entry to the U.S. with a Cleared Bench Warrant

This incident took place in St. Louis, Missouri.

My sister was going to a summer school in St. Louis with an F1 visa when she forgot her pass on the subway and got assigned a ticket. She left the country and I forgot to pay the ticket (I am her brother, a US citizen). When I decided to pay the ticket (about 5 months later), I realized that there was a bench warrant for her arrest. I contacted the court and they gave me instructions to clear the bench warrant. I am in the process of following those instructions. Basically, my sister wrote a letter indicating that she is on the out of town docket, she waives her right to appear in court and will pay the fine. She signed the letter and got it approved by a notary in her country. I will send the letter along with the bond and the clerk told me that when that happens, the warrant will be lifted and the fine will be taken out of the bond amount I will send.

This should all happen by end of February. She is coming to the US at the beginning of April with a tourist visa. Then she will go back and apply for an F1 visa (she already got admitted to a school) to come in the fall. By the time she comes in April, the warrant will have been lifted and the fine will have been paid although I am assuming her record will not have been expunged.

1) Will she have any problems entering the country? Will she be denied entry?
2) Will she be denied F1 visa when she applies for it?
3) Will she have problems in the future (applying for an H1 visa, green card, etc.) due to this incident?

Your help is greatly appreciated.

What type of offense is she charged with? A civil infraction?

i believe she is. she was given a ticket on the subway for not having a pass. is that a civil infraction?

then we forgot to pay, never received any correspondence on the court and she got a bench warrant, which we are in the process of clearing.