Is there a connection between M1V1=M2V2 and Boyle’s Law?
Yes, they are related. The first comes directly from the conservation of number of moles of the solute in a dilution,

$$n_1 = n_2 $$

Since $n = MV$,

$$M_1 V_1 = M_2 V_2$$

The second is related to the conservation of the total number of moles in an isothermal compression or expansion,

$$n_1 = n_2$$

Using the ideal gas law $n = pV/RT$,

$$\frac{P_1 V_1}{R T} = \frac{P_2 V_2}{R T}$$ 

Or $P_1 V_1 = P_2 V_2$.

Again, both are related to the conservation of moles (which by the way, isn't an universal law, since it's broken in trivial situations like the event of a chemical reaction), although the first one refers to solute only and the second to total number of moles.