Task 2: Paper tips
Here follows a list of example papers you can choose for Task 2. You are welcome to choose one or two of these, or any paper that is similar to these.
If you are completely lost, I recommend the following: Pick one paper from the HOPL conference (about A programming language), and one technical paper.
If any of these links are broken, let me know. (But you can probably use Google to find the pdfs anyway...)
Algorithms / Datastructures
A Note on Two Problems in Connexion with Graphs, E.W. Dijkstra, 1959. (Introduces Dijkstra's algorithms for minimum spanning tree and shortest path.) (Quite short, pick another longer paper if you choose this one.)
Quicksort, Tony Hoare, 1962.
Functional Programming
Why Functional Programming Matters by John Hughes, 1984.
Composing Contracts: An Adventure in Financial Engineering by Simon Peyton Jones, Jean-Marc Eber, and Julian Seward, 2000.
A Poor Man's Concurrency Monad by Koen Claessen, 1999. (First paper I ever wrote...)
Parallel Parsing Processes by Koen Claessen, 2004.
The Systematic Construction of a One-Combinator Basis for Lambda-Terms by Jeroen Fokker, 1994. (Quite short, pick another longer paper if you choose this one.)
Mathematics
The Angel Problem by John Conway (of Game-of-life fame), 1982. (Describes a puzzle, and a challenge.)
...
Other classic Computer Science papers
Time, Clocks, and the Ordering of Events in a Distributed System by Leslie Lamport, 1978.
The Complexity of Theorem-Proving Procedures by Stephen Cook, 1971. (Introduces the notion of NP-completeness.)
An Axiomatic Basis for Computer Programming by Tony Hoare, 1969. (Introduces Hoare logic for reasoning about programs.)
A Method for Obtaining Digital Signatures and Public-Key Cryptosystems by Rivest, Shamir, Adleman, 1978. (Describes RSA encryption.)
History of Programming Languages
Take a look at the 10 most popular papers in the History of Programming Languages conference (HOPL). Maybe your favorite language is among them.
10 most popular HOPL papers
You can also look at previous HOPLs if you want to read the paper for your favorite programming language.
External lists of Classics in Computer Science
List of important papers in CS (Wikipedia)
Classics of CS (Google spreadsheet)