Are p‐xylylene and fulvene aromatic?
To decide if a molecule is aromatic or not you must know some rules- 


The Molecule Must Be Cyclic and the system should be conjugated.
The molecule must follow Huckle's rule i.e. it should have (4n+2) Pi Electrons participating in resonance.

3.The molecule must be planar.




For details see-https://chem.libretexts.org/Textbook_Maps/Organic_Chemistry/Map%3A_Organic_Chemistry_(McMurry)/Chapter_15%3A_Benzene_and_Aromaticity/15.03_Aromaticity_and_the_Huckel_4n___2_Rule



Now if you try to draw the resonance structure for your 1st molecule then you will see that 4 electrons are participating in resonance at a time. So the system is not fully conjugated. It will be a cross conjugated system.So both the structures you have mentioned are non aromatic.



Stability is a result of aromaticity. You can not comment that if a compound is stable then it is due to aromaticity.



Here is an image showing resonance in para xylylene.







It can be seen from the resonating structures that some of the resonance structures are not aromatic making the molecule non-aromatic in total.

Any recommendations on making the image better are welcomed.