The 14Be nucleus is a good candidate for having a halo structure. When a three- body model is used to calculate the properties of this nucleus, it relies on a knowledge of the potentials involved and hence on the structure of the underlying two-body subsystem 13Be. Previuosly published calculations showed that, in order to describe 13Be and 14Be simultaneously, 13Be had to be either bound, or have a p-shell ground state, which is not consistent with the experimental data. In this thesis 13Be and 14Be are described as one or two neutrons outside a deformed 12Be core. The idea of the method is that deformation of the core couples the neutron motion with core excitations. The core is treated as a rigid rotor here, and for the neutron-core interaction we used a deformed Woods-Saxon potential. We explore the potential parameters compatible with the known properties of 12Be, 13Be and 14Be. The three-body model for 14Be used a hyperspherical expansion including core degrees of freedom. Compared to the previous works, we find that both 14Be and 13Be are described simultaneously if the 12Be core has large positive quadrupole deformation. The resulting three-body model wave function was used in calculations of reaction observables. The reaction cross section of 14Be on a carbon target at 850 MeV/A was calculated in a four-body Glauber model, after the formalism was extended to include core degrees of freedom. The calculated reaction cross section agrees with the experiment. One-neutron knockout reactions of the Borromean nuclei 6He, 11Li and 14Be are discussed. The integrated cross sections for stripping and diffraction processes are calculated in the four-body Glauber model including core excited components in the wave function for 14Be. The neutron-core relative energy distributions within 5He, 10Li and 13Be following one-neutron removal, are calculated by a spectator model in the eikonal limit. The integrated cross sections and energy distributions for 6He are in agreement with the experiment. The results for 11Li and 14Be breakup demonstrated that the further investigation of the reaction model is needed.