Question regarding traveling on VWP & F-1 Visa

[donsun 38]

Hello,

I have done some research regarding the VSP and F-1 Visa, but I am a bit confused so I'd like to ask my question here:

Currently my girlfriend (Korean Citizen residing in Korea) has been accepted to a 1-month ESL Summer Program at a University in the U.S. In addition to her visiting the U.S., we were also planning to take an international trip, so I was curious to know if the below is possible:

Mid-June: Enter U.S.A. through Visa Waiver Program (Korean Citizen) with intent of just visiting me

Early-July: Visit foreign country, planning a 1-week trip to Europe

Mid-July: Re-enter U.S.A. on F-1 Visa for ESL Summer Program

Mid-August: Leave U.S.A. after ESL Summer Program is over (Potentially stay with me a few weeks after the end of her program)

-Would it look weird for her to enter originally with the VWP first and then with the F-1 upon returning from our Europe Trip?

-I do realize that it is possible for her to enter 30 days prior on F-1, but internationally traveling on F-1 requires an approval from the school, and I don't think she'll have enough time to receive that in advance

-Will there be any issue of her entering on F-1 visa from a country that is not her home country?

-I would also like to confirm that she is able to stay in the U.S. for up to 60 days following the end of her ESL Summer Program

Sorry if something isn't clear or confusing. I'd really like to find out the answer to this, so I'm willing to provide additional details!

Thank you so much!

-donsun