Hi Guy, thank you for your questions!
At the moment we will only support the use of Ni-Mh, Ni-Cd and Alkaline batteries. Generally the problem of Li-ion is that they don't allow high current discharging (a common thing with strobes) and can get damaged, overheat and in some cases even catch fire if they are stressed beyond their limits. We will explore the option of Li-ion and if we find them to be safe we will support them. Your question was added to our FAQ page under No.26 and No.27. For the additional battery compartment please see question No.21 on the FAQ page.
Thank you Alex for answering the other two questions. They are also answered in the FAQ page, No.5 and No.10