Yes.  You are required to schedule an attend a short interview at your nearest US Consulate.

You only need a sponsor if you do not personally have the funds, or a student loan.

An F-1 visa does not provide a direct pathway to permanent residence.

You are required to demonstrate you can support the costs of tuition and living during the first year.  You need to show funds in your account, sponsors account or provide proof of a student loan.

Yes.  International students can apply for jobs on-campus and graduate assistantships.  In addition, Curricula Practical Training (CPT) and Optional Practical Training (OPT) work programs provide opportunities for international students to work during and upon completion of your studies.

The DS160 fee is $160. The SEVIS fee is $350. Both fees are paid online, directly to the US Government.