(1) if she should switch her visa
she can either try to change her status or leave the States and try to get F-1 visa at the US consulate abroad
(2) if she can do it from the United States or if she has to go home first to Ecuador
either. The latter is advisable, because the consulates generally don't like it when people change status in the US, and she may have a problem getting non-immigrant visas later on. However, neither the visa, nor the change of status are guaranteed and may be denied.
(3) when she should start the switch
She would have to start by getting into a US university. The acceptance deadline for foreign students for next fall semester is early January. Once she is accepted (notification in March-April), she will work with the International center at the Uni, they will issue her an I-20 form, with with she will apply for a change of status about 3-4 months before classes begin, or leave the States in July and get an F-1 visa at the consulate.
(4) if she can go home for a visit during this procedure.
She can leave and try to get a visa without applying to change her status. However, if she applied for a change of status, then if she leaves the States while it's pending, she will forfeit the application to change status and will still need a visa. Basically, a waste of money.
How long would this process take?
change of status - 3-5 months. She will not be able to study until the change of status is completed and approved. The other way of going through it is to pick a university where they would allow her to continue her J-1 status in a different category (switch from au pair to an exchange student) instead of switching to F-1. Then, if she is accepted, and J-1 status can be offered to her, she will get a form DS-2019 instead of I-20.
Getting an F-1 visa (how long) depends on the consulate, the consulate's waiting periods for an interview, whether she gets stuck in a name check process, etc.
Is it advisable to even pursue this?
if she really wants to study - yes.
We would love for her to stay on living with us
you can offer her an official letter of support stating that you will provide her with living quarters. However, if there is a suspicion that living quarters will be exchanged for her illegal employment as your part-time nanny, it could be damaging to her.
