We use a different local payment channel in each country to transfer funds directly to the borrower. In Kenya, for example, we use the M-PESA mobile money service to electronically transfer cash into the mobile phone account of each person. M-PESA has an online interface, so we can do this transfer entirely online. Our first loans back in 2009 were disbursed to Masai nomad communities located over a day's journey from any paved road or electricity. It was an amazing experience to send cash electronically from our US bank account to the mobile phones of people in such a remote place, which had been unreachable even by local banks in Kenya. Recent innovations such as mobile phone-based payments are what make a platform like Zidisha feasible.
To address your second question, yes, 100% of lender funds go directly to the entrepreneur that you fund. (We accept optional tips from lenders, and borrowers also pay a 5% service fee for the loans to cover our operating costs.)
It is true that it is incredibly expensive and time-consuming in most developing countries to register a formal business with the government. Most of the entrepreneurs fundraising at Zidisha are in the "informal sector" - though they do very often employ others as a result of the loans.
Zidisha does not provide any kind of business or other training services. We are purely platform for direct P2P interaction, closer to eBay than to the Grameen Bank.