Is it common to find planets orbiting around red dwarf stars to have habitable life?

No one has enough information to answer this question.

My guess: Unlikely

A planet around a red dwarf will not always be tidally locked. But one close enough to the star to have an Earthlike temperature would be. Red dwarfs are very dim, and to have an Earthlike temperature any planet would have to orbit almost right on top of the star. It would experience much stronger solar tides than Earth, strong enough that yes, it would become tidally locked to the star, like the moon is to Earth.

You might have an Earthlike world around a red dwarf if it was itself a moon of a bigger planet. The nearby red dwarf Gliese 876 has a Jupiter-size planet in its life zone for instance, a very big moon might have an Earthlike environment. Alternately some theorists have suggested that even a tidally locked planet could be habitable if the atmosphere was thick enough, but that's more debatable.

By red dwarf, I assume that you mean a spectral class M star, a main sequence star having a mass between 0.08 and 0.45 solar masses. The chief worry is, as you say, about a tidal lock between the rotation and the orbit of a planet that could have liquid water on its surface if it were not tidally locked.

In order for a planet to be habitable, it must have evolved an oxygen atmosphere, which means it must have previously evolved a form of life that converts CO2 to free oxygen. On Earth, that's done by plants. The people who think about this evolution a lot have guessed that it takes about 3 billion years for a planet to become habitable.

That's 3 billion years in which the star's tidal force is slowing down the planet's rotation to lockage with the orbital period.

The incompatibility between the necessary minimum age of the planet and the necessity of not being in rotational tide lock begins at a star mass of about 0.8. And the lower is the star's mass below that value, the greater is the probability of a tide lock for a planet in the ecosphere (liquid water zone).

The red dwarf stars all have very high probabilities of a rotation-orbit tide lock for a planet in their liquid water zones.

There's a way out, however. If the habitable planet is tide locked to a giant planet, which in turn is tide locked to the star, then the giant planet will generate little magnetic field effects because of its relatively slow rotation, while the little habitable planet might have a reasonably short day/night cycle equal to the synodic period of its sidereal periods around the giant planet and the star.

There might be another way out. A tidal lock between a planet's rotation and its orbit doesn't have to be 1:1. It might be 3:2, like Mercury. The planet has a tidal bulge that gets torqued to tightness at every periastron, but successive periastrons torque the opposite bulge from the one that got torqued the last time through.

But there are other problems. Red dwarf stars flare, just like our sun does. But when a red dwarf flares, the flare raises the total luminosity of the star by a much higher percentage than is the case with our sun. So a habitable planet in the liquid water zone had better have a strong magnetic field of its own (to turn away the star's charged particles) and a way to protect any life on it from significant fluctuations in the stellar flux. Like maybe the residents could be living a long ways underground (in the Underdark), or something.

The "good" range of masses for stars that might have habitable planets is

0.8 < M/Ms < 1.42

Or, in terms of absolute magnitude,

5.72 > Mv > 3.22

Or, in terms of spectral class,

K2V ... F1V

The reason for the upper bound in star mass is that stars above 1.42 solar masses turn off the main sequence before the three billion years, needed by a planet to become habitable, can go by. Coincidentally, that's also about where stars switch about in where convective and radiative energy transport prevail (core vs. envelope).

Yes, more so than finding planets around hot blue stars. The planets orbiting these red stars are not always tidally locked, but it should be noted that because red stars are dimmer, the habitable zone around them is much smaller and closer to them then the habitable zone of a star like our sun. This means that unless a planet is in the habitable zone, temperatures will not permit life as we know it. Also, red dwarfs are among the smallest stars, therefore emitting less harmful radiation then some of their larger counterparts; this can only be beneficial to any potential life in the star's system.

the term is tidally locked. and most of the the time a planet near any star will by tidally locked. im not sure this is true for gas planets but it sure is for terrestrial planets. during a planets formation the crust is mostly lava and magma, so the sun pulls on it and creates tides like the moon does to earth. these tides eventually slow down the rotation until it is even with the revolution.

i supposed this would be true for gas planets because they arent solid so i guess the sun would cause tides on them even after the planet has formed.

so id say the majority of the time a planet right next to a star would be tidally locked.

There's no reason planets like the ones you describe couldn't have some form of life. Most scientists believe that liquid water is required for life to start, and your hypothetical planet(s) could easily have that. Nor are such planets around red dwarfs always tidally locked to the star. That would depend on the mass of the planet and whether or not there are other planets in the system.

Since there are no known examples of life on planets around red dwarf stars, I would have to say that it's a pretty uncommon occurrence. Ask your questions again in about 150 years.

firstly it is the red giant not red dwarf [they are the white dwarf]. And the life could not be present on the planets around it because it is very hot and is not much stable.

really good question. i dont see why they couldnt have life. it would just take some weird adaptation. the life would be much, much different than on earth. like something that harvests and has a stable temperature maybe underground. could be nomadic if the planet was out far enough so that days were really really long.

There's enough supposition in this question to allow for any answer without any of them being right, or anyone knowing whether any of them are right.