Anyone have any experience with overseas voting?
I don't, but I can tell you what I found online, and you can ask older bachurim who've been there last year what they did. Or maybe someone here can vet this.
I am a bachur learning in Israel, is that considered living overseas?
Yes:
"Students studying abroad
If you are living overseas for an extended period during an election season and will need to vote absentee, use the Federal Post Card Application (FPCA) to request your absentee ballot. Your voting residence will continue to be your last residence prior to leaving the United States to study abroad.
Your voting residence is your address in the state in which you were last domiciled, immediately prior to leaving the United States.
It is important to remember that your voting residence address listed on the FPCA must be an address in the United States. Placing an overseas address in Section 2 of the form may automatically disqualify you."
https://www.fvap.gov/citizen-voter/voting-residenceThat link is for ALL states. The FPCA lets you choose whether you want them to send the ballot by mail or email, so obviously email will get it to you faster.
If your US address is in NYS, you can find the same information here:
https://elections.ny.gov/military-and-overseas-federal-votingI cannot figure out what format to write my Israel mailing address.
Not clear what you mean by "format". Write the address in English letters - whatever address your family would use to mail you something. Does it go to a POB, or to your name, c/o the yeshiva address?
Can I right my US mailing address if I am requesting a ballot by email?
You should use your US mailing address in Section 2, and your Israel mailing address in Section 3.
The form you should be using is here:
https://elections.ny.gov/system/files/documents/2024/05/federal-post-card-application-2023.pdfYou need to print this form and send it by regular mail, adding overseas postage from Israel. Perhaps there's someone returning soon to the US who can be trusted to carry the post-card to America and drop it in a mailbox, in which case it doesn't need postage and will arrive sooner.
ETA: In most US states, you need to register first, then request a ballot. But if you're overseas and have never registered before, you just need to fill out this federal post card application, which serves to both register you and to request the ballot at the same time.