We only have one planet with life on it to go off and finding life is like looking for a needle in a haystack. So while other exotic forms of life may exist, it would be a lot harder to search for and recognize. And the conditions under which life on Earth exists are understood better so we can look for those range of conditions rather than aimlessly search every conceivable but less likely set of conditions. eg. liquid water. Life can survive two of the extremes of acidity, salinity (saltiness) and temperature but not all three (that we know of) and there has to be a chemical and/or energy disruption of equilibrium of the system. eg. CH4 in the presence of O2 etc. In the needle in a haystack analogy, we are using a magnet to sift through the haystack first because needles that we know of tend to be magnetic. If we dont find anything we might search for bone or ceramic needles using different search methods etc.

Not necessarily. It's more that we know that life can occur on an earth-like planet, and everything else is speculation.

From my understand (degree form YouTube), our understanding of what is needed for life is liquid water and free energy.

Which means earth like is most likely, but there are other alternatives. For example, the moon of Jupiter (Titan iirc) is ice covered but has liquid water beneath the surface, and the gravity of Jupiter should provide the free energy so that’s the Vegas favourite for finding extraterrestrial life within our solar system.