Learn English – How are you finding [something]

Simply "I'll be working late" would be understood that way.

"I'll be working overtime" would also apply, though overtime generally only covers extra hours that are done for extra pay, and not if you get paid a fixed salary regardless.

Actually,

1. I read the paper

does not exactly suggest you read the entire thing. People generally don't read the entire paper. We understand that you typically read the parts that interest you. You might want to specify "I read the entire paper." Someone might congratulate you.

2. I read parts of the paper

is fine. It does mean that you partially read the paper. 1 is implicit about not reading the whole thing, whereas it is explicitly expressed in 2.

3. I read some articles this morning

is also correct. 3 is simply more specific about what you read (articles). However, "articles" does not necessarily refer to ones found in the newspaper. You can find articles in other media, so be careful.

I think you might be interested in skim, glance through, and thumb through:

• skim
  : to read, study, or examine superficially and rapidly; especially : to glance through (something, such as a book) for the chief ideas or the plot
  (M-W)
• glance through something
  to look quickly at the contents of something. I glanced through the manuscript, and I don't think it is ready yet. Would you glance through this report when you have a moment?
  (TFD)
• thumb through something
  to turn the pages of a book, magazine, or a document quickly and only read small parts of it: "Have you read the report?" "Well, I thumbed through it quickly while I was eating breakfast."
  (Cambridge Dictionary)