Interacting Fermi gas provides an ideal model system to understand unconventional pairing and intertwined orders relevant to a large class of quantum materials. Rydberg-dressed Fermi gas is a recent experimental system where the sign, strength, and range of the interaction can be controlled. The interaction in momentum space has a negative minimum at q(c) inversely proportional to the characteristic length scale in real space, the soft-core radius r(c). We show theoretically that single-component (spinless) Rydberg-dressed Fermi gas in two dimensions has a rich phase diagram with superfluid and density wave orders due to the interplay of the Fermi momentum p(F), interaction range r(c), and interaction strength u(0). For repulsive bare interactions u(0) > 0, the dominant instability is a f-wave superfluid for p(F) r(c) less than or similar to 2 and a densitywave for p(F) (r)c greater than or similar to 4. The f-wave pairing in this repulsive Fermi gas is reminiscent of the conventional Kohn-Luttinger mechanism but has a much higher T-c. For attractive bare interactions u(0) < 0, the leading instability is p-wave pairing. The phase diagram is obtained from a functional renormalization group that treats all competing many-body instabilities in the particle-particle and particle-hole channels on an equal footing.