Is it necessary to change the Car's oil filter with the Oil change??

The outside of the filter will always look new, but the inside filtration "paper" stops working after it's filled with gunk and sediment. So yes, it should be changed. Google images "inside of used oil filter".. You'll probably see one cut in half. Plus, it's easy and a few bucks. Lube the ring with fresh oil before you set the new one, hand tighten well or use a wrench to give it a little more turn. Dont jam it in there extra tight though; it's not necessary. Same with the drain plug.

Oil is not opaque yet, you can still see through it. This is the CORRECT time to change the oil, when it is not yet opaque with dirt and wear particles. If you chage the oil and filter before it gets filthy, the engine will last a very long time..

Do you see that ring of flat facets around the top of the filter? That is where the filter wrench goes, if you have a cap-style wrench. if you have a band-style wrench, it just goes around any part of the filter body. The filter turns counter-clockwise to remove it.

Be sure to wet the o-ring on the new one with a little bit of oil, to get a good seal and no tears when you tighten the new one on.

Oil filters are not made of forged steel, they are made of paper and plastic inside. The first source has little on it, but other studies have found inexpensive oil filters can start breaking up internally at less than 5000 miles.

It's just, if not more important, to change the filter.