What does "has not qualms with somebody" mean?
What does "isn't affectionate of somebody" mean?
What does "skipped out on her" mean?
What does "he's pushing for her" mean?


Location, location, location…is reportedly at the heart of the Jennifer Aniston/Justin Theroux split, according to TMZ

An NYC neighbor of "The Leftovers" star told TMZ that while he has no qualms with Aniston, isn't so affectionate of Theroux, and feels sorry for the former "Friends" star
for having been made to live in a [expletive] hole.

Norman Resnicow explained to TMZ how Jen's always been good to him and he actually feels badly for the star, because he believes that Justin apparently forced her to like his NYC pad and then skipped out on her because she wasn't feeling the spot.

The neighbor added that "Everyone knows Jennifer hated the place," and guesses that the "The Break-Up" star obtained top legal assistance to shield herself from Theroux, "who is acting crummy to her like he did to me." He even went on to say that he's pushing for Jen, as she named her most favored dog Norman.

"To have qualms" means to have doubt or worry about a decision or action. I have to disagree with the article in that "qualms" isn't usually used about people.
"I am having qualms about accepting this job."
"I have no qualms about asking Mary to marry me."
For me, it is better to say, "I have no problem with Aniston."
"Isn't affectionate of" means that you are not fond of/don't care for someone. You don't hate them, you just are more neutral. Again, I think this is a poor sentence. We don't usually say that we are affectionate of. Better is "I have affection for" or "The neighbor has less affection (no affection for) Theroux".
"To skip out" means to abandon or run away from. It is always negative.
"He skipped out on her after the honeymoon."
"Tom didn't have any money, so he skipped out of the bill at the restaurant."
"My neighbors moved out of their apartment in the middle of the night. They skipped out of the rent."
"To push for someone or something" means to support or be in favor of a person or action.
"My family can't decide where to go for vacation. I am pushing for Florida." (my choice of destinations is Florida).
"Who are you pushing for in the talent contest?" (who do you want to win the contest?)
"Don't worry about winning the class election. All of your friends are pushing for you.