My comment already gave you the answer; I'm submitting an official answer to give you something to upvote :-)
An elliptic curve is defined within a field; in the case of curve25519, it is defined within the field $GF(2^{255}-19)$; this is a prime field, because $2^{255}-19$ is prime.
So, when we get to the conversion formulas such as $\frac{3 - A^2}{3\cdot B^2}$, this formula is done within the field the curve is defined in.
Because this is a prime field, addition and multiplication can be implemented by addition and multiplication modulo $2^{255}-19$. However, division is trickier; it's typically done by computing the modular inverse of the divisor.
As for your question:
Are there restrictions on which Montgomery curves can be converted to Weierstrass curves?
No, there are no restrictions; all Elliptic curves are isomorphic to some curve in Weierstrass form. The Wikipedia page you gave gives an explicit mapping from a Montogomery curve into Weierstrauss form.
The one glitch is converting the Curve25519 generator, which is defined as $x=9$; they omit the y-coordinate, and hence corresponds to two elliptic curve points (as there are two different solutions on the curve equation with $x=9$). This translates into two different points on the Weierstrass curve (which share the $x$ coordinate as well); you can either say that the conversion is that translated $x$ coordinate, or arbitrarily pick one of the valid $y$ coordinates.