First you have to check the bank about all the documents required for the people who reside outside the country. Banks generally ask for PP copy, Visa copy, offer letter, employee id, pay slips for 6 months etc. In some banks they may ask, to present all these documents at Indian embassy.
• Banks depends on the type of documents you provide
• PP copy, green card, or WP, Tenancy Agreement, Bill(proof of address), Employment offer, Payslips (6 months), Bank statements that shows salary/wages that needs to get credited (6 months), official email id.
• If you are self employed then you may need more details and documents.
• If you are in UK US then you need to show credit reports.
• Processing frees
Well, I have taken such loans, the documents as mention above is required. Apart from the documents, You need to have an NRE account statement of 3 to 6 months from where emi would be paid. Power of attorney in India, depends from bank to banks. The bank which gives you loan need to get notarized from the embassy and should get it stamped in register office.