Is it possible for a planet (with an atmosphere and breathable air obviously) to be super far away from its star but still have a habitable surface temperature just from geothermal activity alone, if so, would there be any bad side effects?
Yes, it is possible that geothermal activity can achieve habitability. In 2018, a group of scientist discovered an extrasolar planet (Barnard’s Star b) orbiting Barnard’s star, an M-type (red dwarf) that is 6 light years away. It is at least 3.2 times as massive as Earth and experience average surface temperatures of about -170 °C (-274 °F) making it both a "Super-Earth" and "ice planet". Based on this, many have concluded that the the planet would be hostile to life but according to new studyref. by a team of researchers from Villanova University and the Institute of Space Studies of Catalonia (IEEC), it was predicted that the planet has a hot iron/nickel core and experiences enhanced geothermal activity and it can thus support life.
The planet orbits Barnard’s Star at a distance of about 0.4 AU, so it only receives about 2% of the energy from its star, so others hypothesized that life was not possible. However, the recent study shows there are still possible scenarios in which subterranean life could exist. These include the possibility that while the surface may be icy cold, geological activity might allow for life beneath the surface. They quote:
Geothermal heating could support "life zones" under its surface, akin to subsurface lakes found in Antarctica. We note that the surface temperature on Jupiter’s icy moon Europa is similar to Barnard b but, because of tidal heating, Europa probably has liquid oceans under its icy surface.
I'm going to make the assumption that you mean life other than humans. Humans can survive anywhere with enough technology, even frozen, lifeless rocks. We don't even need a planet, as our experience with long-term space habitation has shown we need gravity, and at some point in the relatively near future we will be able to build habitats which will spin to simulate gravity. On your proposed planet thermal energy would be useful as it would be a way to generate electricity and heat habitats, but we could use nuclear reactors or other technology to produce electricity if that wasn't available.
All you need for life is some building blocks and most important, a form of energy. Light is only one source of energy, on our planet most life is reliant on the sun in some way, but even on our planet we have found life that have evolved to live off heat. The best example I can think of is microbes that live near deep hydrothermal vents, and the animals that feed off them. There's a whole ecosystem near underwater volcanic vents which is completely independent of light. So it is possible that life could evolve on a planet that still has a molten core and volcanic activity.
Arguably we already know of a planet where internal energy from the planet sustains life. According to the National Oceanic and Atmospheric Administration:
Organisms that live around hydrothermal vents don't rely on sunlight and photosynthesis. Instead, bacteria and archaea use a process called chemosynthesis to convert minerals and other chemicals in the water into energy. This bacterium is the base of the vent community food web, and supports hundreds of species of animals.
In the case of Earth, geothermal energy is known to work hand in hand with geochemical energy. The heated water facilitates reactions that produce the reactive chemicals, such as hydrogen, hydrogen sulfide, or even dissolved ferrous iron from mafic rock that serve as fuel sources for biological processes. Such biological processes are widely seen as a model for possible life in subterranean oceans in ouer Solar-System moons, where the oceans are supported by geological processes that (given the necessary minerals) may also generate chemical reactions similar to those evident on Earth.
Geothermal energy can be extracted from the temperature difference (on the surface vs in depth) but this needs a large organism more like a large underground tree with specific structure. A small cell would have the same temperature over it and could not use the gradients.
But some microorganisms, if required for the beginning of evolution, could evolve using chemiosynthesis first.