Best way to send money to India is through remittance brokers like Placid, Transfast etc. Make sure to shop for company giving you the best value not just best rate. Some companies give you highest possible rate but charge higher fees. So make sure to look for the one giving you best value.
Yes. If money is transferred using companies supporting cash as payout option. Few examples of companies supporting cash payout options are Xoom, Azimo and World Remit.
There is no limit on money one can transfer to India given they can prove money is acquired through legit means and all taxes are paid. Even though there is no legal limit every money transfer company have imposed daily and monthly transfer limits. These limits vary from company to company.