If Mars orbited the Earth how distant would it have to be to cause the same tides? If it were possible to replace the Moon with Mars, how distant would it have to be to essentially create the same oceanic tides as the Moon currently does? Mars seems to be roughly 3 times the mass of the Moon, so does that mean it should be 300% the distance?

Furthermore, would the increased distance cause any issues with Earth's orbit around the Sun or potentially cause some sort of situation like Charon and Pluto where the centre of mass is between them?
The Tidal acceleration between 2 bodies is calculated with this formula:

$$
a_T = \frac{2GM_MR_1}{Dm^3}
$$

Where $M_M$ is Mar's mass, $R_1$ Earth Radius and $D_m$ the distance to the Moon. If you equal this to Moon's Tidal acceleration you will get $D_M$ as distance to Mars to get the same Tidal acceleration having $\frac{M_M}{M_m}=8.73328184501$:

$$
D_M = \sqrt[3]{8.73}D_m\simeq2.06Dm
$$