Theory:

     Each morning, when the routine of opening his shop was completed, it was the proprietor’s custom to perch on a high stool, behind the counter, unfold his morning paper, and digest the day’s news. As he read he would smirk, frown, reflectively purse his lips, knowingly lift his eyebrows, nod in grave agreement. He read everything, even advice to the lovelorn and the detailed columns of advertisements.
Explanation:

Mr Purcell used to open his shop every morning. Once he opened the shop, his daily routine was to sit on a high stool behind the counter. He sat on a high stool because he was short and wanted to see the customers when they entered the shop. Later he would unfold his morning paper, and digest the day’s news. The term "digest the day's news" implies that he would take necessary time to understand what was given in it, and also, he would read every nook and corner from the newspaper. While he was in the pet shop, he'd have plenty of time to read the newspaper till the customer arrives.

Then the narrator mentioned the different ways and expressions Mr Purcell used to read the newspaper. Usually, a newspaper consists of varying news. So while reading the newspaper, he would show many expressions on his face. As he read the newspaper, he would smirk at times. When he saw some intense arguments or annoying things, he would raise his eyebrows and shown dissatisfaction on his face. Also, he would pursue his lips. The phrase "pursed his lips" refers to the tightening of the lips to make a rounded shape. It was frequently done to show an expression of disapproval. In addition, if he read any serious issue, he would nod his head. These things suggest that Mr Purcell was quite interested in reading the news from the newspaper. He'd react as if things were reported in the newspaper.
 
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Mr Purcell reading newspaper

Furthermore
, he would read everything, and even he would read the advice given to the lovelorn. The term "lovelorn" referred to a person who felt miserable because someone had stopped loving them. He also used to read the advertisements from the newspaper. People usually read their favourites or most exciting stuff from the newspaper. Some people would skip the newspaper's advertisement section. Mr Purcell, on the other hand, was quite different, and he would read the entire advertisement column. Moreover, he would not leave anything in the newspaper unread. It could be because he was curious about things around him, or else he would have plenty of time to read the newspaper.
 
Meanings of the difficult words:
 
S.No
Words
Meanings
1
Routine A usual or fixed way of doing things
2
Proprietor A person who owns and usually manages a business
3
Custom A way of behaving or a belief that has been established for a long time
4
Perch To sit on or near the edge of something
5
Digest To read or hear new information and take the necessary time to understand it
6
SmirkA smile that expresses satisfaction or pleasure about having done something or knowing something that is not known by someone else
7
FrownTo bring your eyebrows together so that there are lines on your face above your eyes, often while turning the corners of your mouth downwards, showing that you are annoyed, worried, sad, or thinking hard
8
Purse his lipsTo bring your lips tightly together so that they form a rounded shape, usually as an expression of disapproval
Reference:
National Council of Educational Research and Training (2007). Supplementary. I Want Something in a Cage - L E Greeve (36-42). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.