She has won awards such as....
Costume Designers Guild Awards 2015: CDG Award Outstanding Contemporary Television Series
Costume Designers Guild Awards 2014: CDG Award Outstanding Contemporary Television Series
She has worked with other shows such as Scandal
This shows time period is set in 2011- now
They do not relate much because the family in shameless are struggling to make wage and can't afford to buy new nice clothes all the time while the families in the pictures above seem to have very nice clothes and look very clean.
Some trends that Lyn Paolo used were holey jeans, at different points throughout the season, several characters wear the same clothes, they try to repeat looks. Their aunt makes sweaters. They put holes in clothes, thrashing it, pulling it out of shape. Making them look used and owned by someone else.
I don't think they missed any trends when it comes to a poor family living in Chicago. They made everything look good and like they actually didn't have a lot of money, they live in a run down house with several mouths to feed so they can't afford new clothes or to look nice. They thrift shop and borrow clothes from each other. Lyn Paolo made them look like a poor family in Chicago.
People everywhere have started wearing ripped jeans and oversized sweaters, but they have been doing this for a long time. I don't think Shameless has influenced fashion very much since people already wore what the characters have been wearing for a while now.