I think you might be talking about The Illustrated Man, a collection of stories by Ray Bradbury. It has gone through many editions; does any of these covers look familiar?
The first story you mentioned, about the stranger who gives himself away by not pulling up his pants legs when he sits down, sounds like Bradbury's short story "The Fox and the Forest" (aka "To the Future"), which was also the answer to this old question; however, the stranger is a human time-traveler from the future, not an alien. The X Minus One radio adaptation is available at the Internet Archive. Here is an excerpt:
Susan and William sat and ordered a drink.
The stranger was examining their clothes, their hair, their jewelry—the way they walked and sat.
"Sit easily, said William under his breath. "Look as if you've worn this clothing style all your life."
"We should never have tried to escape."
"My God!" said William, "he's coming over. Let me do the talking."
The stranger bowed before them. There was the faintest tap of heels knocking together. Susan stiffened. That military sound!—unmistakable as that certain ugly rap on your door at midnight.
"Mr. Roger Kristen," said the stranger, "you did not pull up your pant legs when you sat down."
William froze. He looked at his hands lying on either leg, innocently. Susan's heart was beating swiftly.
"You've got the wrong person," said William quickly. "My name's not Krisler."
"Kristen," corrected the stranger.
"I'm William Travis," said William. "And I don't see what my pant legs have to do with you."
"Sorry." The stranger pulled up a chair. "Let us say I thought I knew you because you did not pull your trousers up. Everyone does. If they don't, the trousers bag quickly. I am a long way from home, Mr.—Travis, and in need of company. My name is Simms."
"Mr. Simms, we appreciate your loneliness, but we're tired. We're leaving for Acapulco tomorrow."
"A charming spot. I was just there, looking for some friends of mine. They are somewhere. I shall find them yet. Oh, is the lady a bit sick?
"Good night, Mr. Simms."
They started out the door, William holding Susan's arm firmly. They did not look back when Mr. Simms called, "Oh, just one more thing." He paused and then slowly spoke the words:
Susan shut her eyes and felt the earth falter under her. She kept going, into the fiery plaza, seeing nothing.
"The Fox and the Forest" has appeared in other compilations, but The Illustrated Man seems the most likely. You also mentioned a story about "robots being used in the home". That could describe a lot of stories, but if it was in The Illustrated Man, it could be another Bradbury short story, "Marionettes, Inc.", which was also the answer to this old question. "Marionettes, Inc." is available at the Internet Archive, both as a scan of the original publication in the March 1949 Startling Stories and as an X Minus One radio play; it was also an episode of The Ray Bradbury Theater, available at YouTube. Here is the Wikipedia plot summary:
Friends Braling and Smith take a walk one evening, much to the surprise of the latter, as Braling's wife generally tries to keep him from doing things he enjoys. Braling reveals to Smith that he has been using a robot duplicate of himself, Braling Two, to fulfill his obligations as a husband while he pursues his personal interests. His wife is completely unaware of the duplication. He plans to visit Rio de Janeiro for a month while his robot covers for him at home.
Smith, fascinated by this new (and technically illegal) technology, considers buying a duplicate to deal with his own wife, Nettie, who in the last month has been overly affectionate. Braling gives him a contact card for Marionettes, Inc. Smith goes home and finds his wife sleeping. He briefly wrestles with the ethics of deceiving his wife before getting out his bankbook to set aside the $8,000 he would need to purchase the duplicate. To his surprise, Smith finds that $10,000 is missing from their account. He checks the sleeping Nettie and realizes that she herself is a robot duplicate of his wife.
When Braling tries to return home and hide Braling Two, the robot resists him, expressing a love for his wife. Realizing that the duplicate is trying to replace him, Braling panics. The story ends in the Bralings' bedroom with "someone" kissing Mrs. Braling affectionately.
If The Illustrated Man is really the book your teacher was reading, you might recognize some of the other stories from the plot summaries on the Wikipedia page for this collection.