Proper fractions are the fractions in which the numerator is less than the denominator like $\frac{2}{5},\;\frac{13}{19}$ etc.

Improper fractions are the fractions in which the numerator is greater than the denominator like $\frac{6}{5},\;\frac{23}{19}$ etc.

Mixed fractions are the fractions in which there is a whole and a fractional part. For example, $1\frac{2}{5},\;2\frac{3}{7}$, etc.

Yes, unlike fractions can be equivalent if converted in simpler terms. For example, $\frac{1}{2}$ and $\frac{2}{4}$.

Like fractions can be called similar fractions and unlike fractions can be called dissimilar fractions.