Why reactivity increases down the group?
When an alkali metal atom reacts, it loses an electron to form a singly positively charged ion e.g. Na Na+ + e- (in terms of electrons 2.8.1 2.8 and so forming a stable ion with a noble gas electron arrangement).
As you go down the group from one element down to the next the atomic radius gets bigger due to an extra filled electron shell.
The outer electron is further and further from the nucleus and is also shielded by the extra full electron shell of negative charge.
Therefore the outer electron is less and less strongly held by the positive nucleus.
This combination of factors means the outer electron is more easily lost, the M+ ion more easily formed, and so the element is more reactive as you go down the group.
The reactivity argument mainly comes down to increasingly lower ionisation energy down the group.