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You can apply now and go from there. We need a two year history. We don't need two years on the job unless in certain situations. Loan officer will ask about the credit inquiries and as long as there is no new credit or a sign showing that you're heavily applying for credit and keep getting denied, it SHOULD be okay.
That is a loaded question. Please apply through a local lender or broker and they would be able to answer your question. That question is dependent on down payment, credit score, and debt to income.
Conventional with 3% down and FHA has 3.5% down. Conventional will only take you to 45% debt to income ratio and FHA will take you to 56.99% debt to income ratio, if the lender has no overlays. What your friend meant is a lender credit. No need for special lenders, all lenders will do it. Lender gives out a credit (dependent on loan amount) by raising the interest rate. You can always ask the sellers as well to pay for some closing costs in the form of seller credit and ask the lender to raise the interest by 0.25% - 0.5% to cover the rest of the closing costs while you just pay for the downpayment.