Does the atom get a net negative charge when it emits an alpha particle? And positive for beta?

a)When an atom emits an alpha particle, the atom's mass number decreases by four due to the loss of the four nucleons in the alpha particle. The atomic number of the atom goes down by exactly two, as a result of the loss of two protons – the atom becomes a new element.

I dont know about whether beta particle is emitted whenever alpha particle is emitted but there is no net charge on the newly formed atom undergone alpha emittion.

b)An unstable atomic nucleus with an excess of neutrons may undergo β− decay, where a neutron is converted into a proton, an electron and an electron-type antineutrino (the antiparticle of the neutrino):

n → p + e− + νe

This process is mediated by the weak interaction. The neutron turns into a proton through the emission of a virtual W− boson. At the quark level, W− emission turns a down-type quark into an up-type quark, turning a neutron (one up quark and two down quarks) into a proton (two up quarks and one down quark). The virtual W− boson then decays into an electron and an antineutrino.

The smallest unit of a matter is an atom which has the two basic charged particles, which are oppositely charged. The electron being negative and proton positive is only a name historically given to the two charges so as to make it clear that both are equal in magnitude but opposite in nature. They could have been assigned the opposite charges also (In fact, some believe, that would have been better since electron will then be positively charged which is most commonly encountered in most of the reactions except nuclear reactions)

The only thing that changes is the amount of electrons. A negative Ion will turn into a positive Ion only when it gives up electrons. Adding a proton would be nuclear.