Kitaev's 0-π qubit encodes quantum information in two protected, near-degenerate states of a superconducting quantum circuit. In a recent work, we have shown that the coherence times of a realistic 0-π device can surpass that of today's best superconducting qubits (Groszkowski et al 2018 New J. Phys. 20 043053). Here we address controllability of the 0-π qubit. Specifically, we investigate the potential for dispersive control and readout, and introduce a new, fast and high-fidelity singlequbit gate that can interpolate smoothly between logical X and Z. We characterize the action of this gate using a multi-level treatment of the device, and analyze the impact of circuit-element disorder and deviations in control and circuit parameters from their optimal values. Furthermore, we propose a cooling scheme to decrease the photon shot-noise dephasing rate, which we previously found to limit the coherence times of 0-π devices within reach of current experiments. Using this approach, we predict coherence time enhancements between one and three orders of magnitude, depending on parameter regime. ζ-mode) [22]. Nevertheless, we found that the 0-π qubit still has the potential to outperform state-of-the-art superconducting devices. Below, we propose a method to further enhance the coherence time by orders of magnitude by cooling the ζ-mode.However, as can be expected, the price of intrinsic noise protection in the 0-π qubit is that it is difficult to perform logical operations on this device. In particular, protection from noise comes in part from the exponentially small overlap of its logical wave functions. As a result, matrix elements of local operators between the two logical states will also be small, thus resulting in extremely slow gates. In [20], Brooks et al proposed a universal set of protected logical operations based on coupling to an ultra-high impedance LC oscillator. However, these operations were based on an idealized model of the qubit and with parameters that are difficult to realize in practice. Further work is required to determine the potential of this approach in a more realistic setting.Motivated by the prospect of realizing 0-π qubits in the near term, we investigate alternative approaches to measurement and control with lower experimental complexity. The operations we propose are not protected in the same sense as those proposed in [20], because they rely either on operating the device in a regime where the qubit is not fully isolated from the environment, or they make use of excited states outside the qubit manifold. In particular, we develop a single-qubit gate based on a multi-level excursion through higher energy levels. Nevertheless, we hope that these schemes will be useful for both characterization and control of 0-π qubits in near-to-medium-term experiments.This work is organized as follows. In section 2, we introduce the 0-π qubit and provide a simplified effective model for the 0-π circuit with only a single degree of freedom. In section 3, we discuss general coupling strategies for qubit co...