What is "upsies"?

Can I use "cut" instead of "chop"? How different them?

In this case, it would sound unnatural to use "cut" instead of "chop". This is because to "cut" something usually means to make an incision using something like scissors or a knife, but to "chop" implies a bigger force, using bigger tools. When talking about wood, "chop" is the usual verb to use because it requires the use of an ax, which is a very heavy duty tool. Ex: He chopped down the tree. Ex: I am chopping up the vegetables. Ex: The girl cut the paper with scissors.

Could you teach me the meaning of "spy on"? Is it different from "stakeout"? And do you use "spy on" commonly?

To "spy on" means to watch someone or something secretly, often in order to discover information about him, her, or it. It is different from the word "stakeout" because a "stakeout" is generally just watching an area or building, not necessarily a specific target. A stakeout is also usually something that is done in relation to crime. Whereas "spying on" someone can be used generally. I would also say that "spy on" is a generally more common phrase that you would hear in regular conversation than "stakeout". Ex: I need to spy on my boyfriend to figure out what to get him for his birthday. Ex: How did you know I went shopping? Are you spying on me? Ex: My mom is always spying on our neighbors. Ex: You don't have to spy on me, you can just ask.

What's the "trials of apartment hunting?"

"Trials" is often used to mean a thing, person, or situation that is testing, difficult, or troublesome. Thus, "trials of apartment hunting" can be understood to mean the "difficulties of apartment hunting." Ex: Once you graduate, you will experience the trials of work life. Ex: The trials of parenthood can be very stressful.

"You see through me" and "you can see through me", what's different between these two? 

There is not much of a difference between "you see through me" and "you can see through me", except that "can" emphasizes one's ability to do something. Without "can", there is less emphasis on the ability of doing something, however, the overall meaning is not changed.

How can I use "as though"?

You can use "as though" to introduce something that you think is true, which is how it is used here. You can also use "as though" to introduce a hypothetical comparison to a situation. Ex: I feel as though you don't like me, because you frown when you see me. ("As though" used to introduce something that you think is true) Ex: My hands felt cold, as though I had been touching ice. ("Hands feeling cold" being compared to the hypothetical situation of "touching ice" using "as though")