The paper describes the possibility of producing a focused parametric X-ray radiation (PXR) without applying any special X-ray optics. The PXR is emitted by relativistic charged particles that are channeling along a bent crystal. The PXR emitted from the whole length of the bent crystal is brought into focus. Some properties of focused PXR are estimated for typical experimental conditions, its possible applications are discussed. Besides, the feasibility of diffraction of parametric X-ray radiation emitted by relativistic particles in a bent crystal is described for the first time. The PXR generated at one set of crystallographic planes may be diffracted by another set of crystallographic planes in the same bent crystal. In the example being, the PXR is emitted in the backward direction and undergoes diffraction at a right angle. After diffraction, the PXR escapes from the thin crystal and becomes focused. Some properties of the diffracted focused PXR are estimated for typical experimental conditions. The experiment for observation of focused non-diffracted and diffracted PXR is proposed. Application of focused PXR for online control of the bent crystal and paricle beam state and the bent crystal alignment is proposed. Besides, possibilities for diffraction, extraction and focusing of crystal undulator radiation, as well as focusing of channeling radiation from a bent crystal are proposed. The installation of X-ray detector(s) in the vicinity of Bragg direction(s) is proposed in forthcoming experiments with crystalline undulator for observation of undulator radiation and online control of the undulator and particle beam state and

also undulator alignment.

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