Unable to Update Several Packages

In the past two weeks, I could not update my Ubuntu system 14.04 LTS. In particular, every time I turn on my computer, the following window pops up.

After I click "Install Now", it asks for my password. After I type my password, the following window pops up.

If I click OK, then nothing happens and next time the same thing repeat. If I click "Settings...", the following window pops up.

However, I am not sure what to do with it.

Did anyone have similar experience before? How to fix it, please? Thank you!

Update:

After typing sudo apt-get update as suggested in the comments, I got a long list and the following error message.

Fetched 3,393 kB in 40s (84.1 kB/s)                                            
W: GPG error: http://cran.rstudio.com trusty/ Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 51716619E084DAB9
W: Failed to fetch http://ppa.launchpad.net/piotr-zagawa/ma2/ubuntu/dists/trusty/main/source/Sources  404  Not Found

W: Failed to fetch http://ppa.launchpad.net/piotr-zagawa/ma2/ubuntu/dists/trusty/main/binary-amd64/Packages  404  Not Found

W: Failed to fetch http://ppa.launchpad.net/piotr-zagawa/ma2/ubuntu/dists/trusty/main/binary-i386/Packages  404  Not Found

E: Some index files failed to download. They have been ignored, or old ones used instead.

And there is also the following errors:

Err http://ppa.launchpad.net trusty/main Sources                               
  404  Not Found
Err http://ppa.launchpad.net trusty/main amd64 Packages                        
  404  Not Found
Get:12 http://archive.ubuntu.com trusty-updates/universe Sources [133 kB]      
Err http://ppa.launchpad.net trusty/main i386 Packages                         
  404  Not Found