Can I record a channel while watching another?
The device only has one tuner, While recording a channel you cannot change it to a different one. If your TV has a DVB-T tuner you can record a channel from the device and watch a different channel with the tuner of the TV
How can I know the serie of my DVB-T to download the correct firmware file?
The series refers to the first three digits of the serial number. You can find this number on the back of the device or in the packaging of the product.