What I had in mind was a huge being (moon/planet sized) that lives and moves through space, now could a living being do that? Maybe it could feed on light and radiation from stars? And would a being be able to move in the vacuum of space, if so, how?
Yes, surely. Although they would be vastly different from those we know, it is perfectly possible for a living being to have a skin comparable to a spacesuit, or a hard, ship-like shell.
They could 'photosynthesize' (although not exactly the way plants do) from stellar light, but probably they would still need to consume asteroids (and spaceships) to take in material and grow.
They could move with some type of reaction engine (rocket). It could be a simple pressurized gas forced out, chemical rocket, electric engine, or biologic mass driver, (a hand throwing stones).
So theoretically it is possible, but it is hard to imagine the biology and evolution of such a being, and some part of it would resemble 'technology' more that 'life'.
Freeman Dyson postulated a "Dyson Tree" planted on the core of a comet and extending outwards into space to extend light gathering leaves or some equivalent photosynthetic organ. Humans and animals could live within the bodies of the trees as symbionts, breathing the oxygen and providing carbon dioxide and nutrients in the form of wastes. In theory there is little to prevent the Dyson tree from growing to any arbitrary size, and the tree can use light pressure on its leaves to slowly move about in the reaches of deep space.
A forest of Dyson trees near a planet
Tardigrades, also known as "water bears," are microscopic creatures known to survive extreme conditions such as vacuum, extreme cold (1 degree kelvin) extreme heat, ionizing radiation...
Earth is a "living" being. Kind of.
At least if you allow some freedom in the definition of "live". While it is clear that Earth contains living beings which fed on sunlight (photosynthesis->plant->animal), you can also view Earth itself as some kind of organism (Gaia theory). If someone here cringes for the word "organism" and imagines new-agers with peace symbols smoking weed bowing to a natural godess, you can replace that with the more technical term: "feedback loop".
Planet-sized beings (at least encompassing a whole planet) are to our current knowledge impossible. After a few kilometers depth the pressure deforms anything living in solid material and solves too much disinfecting gases in fluids, so that does not work. This does not mean that living being can grow to gigantic sizes: The USA has a gigantic honey fungus in the Malheur National park in Oregon which has a weight of over 600 tons.
Small living things can survive in space.
Small living things like microorganism are in fact able to survive long periods in vacuum and radiation. We have found by experience that in the capsules microorganisms feel quite well and build biofilms which are very resilient, some types of microorganism are extremely resilient even against radiation and vacuum and could theoretically survive being pushed in space in a meteorite by an impact and survive reentry.
I am not sure it would fit your criteria bu imagine an earth-like planet covered by a single large organism. With the planet's mass it could have it's own atmosphere and possibility a magnetosphere which would protect it from space. Like all life on our planet it would have to absorb energy from the sun and use material from the planet to form itself. It would probably not be able to move itself.
If you want a deep space organism you are going to run into the problem of lack of energy and lack of matter to convert into tissue.
As a side note if you want a organism which has grown to the size of a planet it will have to have consumed a planet worth of matter but most of the interior matter could be non living in the same way much of the tissue in the centre of many trees does not have any biological activity but provides structure for the living part of the tree.
Unlikely for the size
Life finds a way of adapting, living in the vacuum of space wouldn't be kind on creatures who have evolved to a gravity but I dare say life could find a way.
However you need the material to grow and become planet sized. On earth plants use the carbon in the air and nutrients in the soil to grow but if your creature is planet sized (not just something living on the surface of a planet) then you need to acquire all that material from somewhere. Space is largely empty so I can't imagine it being very likely a species would survive if it relied on finding that much material to grow.
Very much depends upon how you define a living being.
Humans, with special suits can live in space, with protective shelters and special nutritious foods in packets.
What you're imagining is a living being that survives on light, can travel through vacuum, and is the size of a planet or moon.
While I've never heard of such a being yet, we can't rule out any possibilities. There might be "living beings" out there in the ocean of stars.
So, currently, no, there appears to be no such a being. But who knows what's out there!
Such a being would have evolved to survive on radiation. See how our trees feed on sunlight.
Such a planet sized being would've evolved in a way that it can adjust its shape, or eject mass from its own body to aid movement in vacuum.
It might be orbiting a star somewhere, and we might have even detected it but didn't know it was a living thing.
Because one of the criteria to being alive is breathing, no living object can be alive in a vacuum. However an object with the size of a planet could keep its own air around it. Keep in mind that said planet would have to be big enough to actually have an atmosphere which means that even something the size of our moon would not be able to live in space.