This article investigates novel adaptive self-interference cancellation solutions and the total integrated cancellation performance of a mobile single-antenna inband full-duplex transceiver. First, novel self-adaptive digital self-interference cancellation algorithms are described, with an emphasis on tracking of time-varying self-interference coupling channel in a mobile device as well as on structural ability to suppress also nonlinear self-interference with highly nonlinear mobile power amplifiers. This leads to an advanced self-adaptive nonlinear digital canceller which utilizes a novel orthogonalization procedure for nonlinear basis functions, together with low-cost LMS-based parameter learning. The achievable self-interference cancellation performance is then evaluated with actual RF measurements using mobile device scale RF components, in particular a highly nonlinear PA. The measurements also incorporate a novel self-adaptive RF cancellation circuit in order to realistically assess the total integrated cancellation performance. The reported results show that highly efficient self-interference cancellation can be achieved also in a mobile device, despite a heavily nonlinear PA and limited computing and hardware resources. The proposed cancellation solutions, when integrated together, show that 100 dB of self-interference can be cancelled using a 20 MHz LTE waveform, while the SI can be attenuated by over 110 dB with a narrower bandwidth of 1.4 MHz, all measured at 2.4 GHz ISM band. Furthermore, these results are achieved using a highly nonlinear transmitter power amplifier and fully adaptive canceller structures which can track a rapidly changing coupling channel in a mobile full-duplex device.