Hi. I would like to know if i have to change this enginen support. Its from a volvo v50 2012 d2 1.6 engine.the left side is in same condition.

 

It's hard to say from just that photo. The rubber bushings can show surface cracks long before their performance is compromised by the failure of the rubber. I'd suggest having someone you trust (!) cycle the transmission through D-N-R-N-D a few times (or if it's a manual, lightly engaging the clutch as if gingerly taking off from a stop), and see if there is any unusual movement in the motor mount(s). If one or both is bad, you will most likely be able to tell as those cracks will "open up" as the motor mount flexes too much.

 

someone told me that this type of support has oil in it and when the oil leakes it means to change the part.The problem is i dont see any oil at all. but oil can be clean in time.
the engine does shake a lot and it transmits to the steering wheel. the weird part is i enter another car from 2009 volvo s40 with the same bad shaking of the engine but the steering wheel does not shake at all. but the body of the does shake.
Could it be somewhere a part of the engine touches the frame of car?

 

I'm not at all familiar with that mount (or your particular engine) since it's so different from my 2005 2.4i, but I doubt that the front and back motor mounts are oil filled. At any rate, doing the (easy) test I suggested before will make it pretty easy to see if one or more of the mounts is defective. You could see excessive motor movement even if the end mounts are good, if one of the other mounts is worn out. There's really no way other than visual inspection, and testing them under some engine torque to check them though.

There are a lot of other things that can transmit shaking through the steering wheel, including the control arm bushings (being worn out), a bad CV axle (pretty common, too), or anything that might cause a misfire (less likely in a diesel, but a bad injector could do it).

Sometimes it's easier to just swap out a suspect component if it's a "wear item", and doesn't cost too much (it won't) and is easy enough to change out (I believe it is in your case).