Hello Guys.
Im a total beginner to my Jag X-Type 2003 2.5 V6.

Meanwhile trying to change engine oil I inspected the bottom of the car and noticed in the transmission shaft traces of oil.
What are this parts and should I worry (no oil traces seen on the road though)?

 

I think by "in" you mean "on" the transmission shaft. I say clean it off as completely as possible, and then check it again after a hundred miles to see if it is oily again. Then try to determine if it is transmission fluid or engine oil.
As a general precaution, if you bought this car used and are not sure about the repair and maintenance history then you should get someone to check and maybe replace the transmission fluid. I was spooked to find there is no transmission dipstick on my car and that it is pretty tricky trying to confirm the transmission fluid level or quality.
My regular mechanic refused to do it and referred me to a specialist who took several weeks trying to confirm an acceptable transmission fluid besides the Jaguar specification product which was running $45/qt.
P.