Your employer will apply for you, you cannot apply directly and on your own. Your job would be to find and employer willing to sponsor you for an H1B visa. Read the job advertisements carefully, if it specifies that the applicant needs to be an US citizen or greencard holder they are not interested in sponsoring any work visa.
no, definitely not. first you need a US employer who is not only willing to hire you, but also willing to file the proper paperwork with USCIS in the US. once that’s processed and approved, you can apply for the visa, but not before. at this point, if you had an employer who did file for you, you wouldn’t be eligible to work on that visa before October 1.