Is there air outside of earth atmosphere? If not, could we feel heat coming from sun?
We can most definitely feel heat in space.
As @aystack said, on earth heat transfer is through contact, convection or radiation. Convection relies on the movement of air or some other fluid, so that will only work inside a spacecraft or spacesuit. Transfer of heat through contact means that, if you touch something that is hot or cold, you will definitely feel it.
Radiative transfer of heat in space works in the same way in which you feel the heat of a roaring fire, or an electric bar heater. Photons travel from the source to us, enabling us to feel the heat. Photons travel through vacuum even easier than through air - if they didn't, we would not even be able to see the sun or stars.
It is because the photons travel from the sun through vacuum that we are able to feel the heat of the sun here on earth. Spacecraft also have to make sure that they do not overheat when the sun shines on them. With some spacecraft that means installing massive sun-shields. For example, the James Webb telescope, due for launch in November, uses a 5-layer, tennis court-size sunshield to keep cool. This shield is made of reflective material, so the sunlight is reflected away from the telescope.
The Parker Solar Probe, which flies to within about 6 million km of the sun (roughly a 10th of Mercury's distance), carries a massive carbon-composite shield that will reach temperatures of 1350C.
The pressure in space is very low as there are very few atoms per unit volume (compared to the atmosphere).
As a result, convection and conduction do not work for heat transfer, but radiation still works. Without sunlight, there is only 2.7 K background microwave radiation from big bang, so very cold (-270 deg Celsius). With sunlight you get quite warm, because the only way for you to loose temperature is again to radiate it - vacuum is a good isolator.
In this context, it is worth to mention that due to the low pressure around you, the boiling point is very low and liquids in your body like blood will boil very fast. There are interesting questions and answers about what actually happens if an astronaut takes off his helmet. Here is just one from another forum as an example https://www.quora.com/What-would-happen-to-an-astronaut-who-took-their-helmet-off-in-space-for-a-few-seconds.
I would say yes, one should be able to feel heat in outer space. Heat transfer can be due to contact, convection, or radiation. Although there is practically no air, in outer space there is light, or more precisely, electromagnetic radiation (visible, infrared, etc.) from the sun. So in principle at least, one should be able to feel heat from the sun in outer space.