The low-energy 6He+p, 6He(p,n)6Li(1+,0+), and 6He(p,α)t reactions are studied in the framework of a microscopic multicluster model. The 6He, 6Li, and t wave functions are calculated variationally with microscopic three-cluster structures. The different thresholds are fairly well reproduced. The model provides the experimentally known states and resonances of 7Li up to Ex=12 MeV except the second 7/2- state. A 3/2-;T=3/2 resonance is obtained which should correspond to the experimental 3/2-;3/2 resonance at Ec.m.=1.27 MeV. This resonance might have a halo structure. The 6He(p,n)6Li(0+; 3.56 MeV) cross section should be strongly affected by this resonance. Cross sections are also calculated for the 6He+p elastic scattering and for the 6He(p,α)t transfer reaction. The 6He+n elastic phase shifts are determined with a similar model and provide the isobaric analog 3/2- ground state of 7He and a 1/2- excited state.