I became a permanent resident in July of 2013. But, in 2013, I stayed in the U.S. for only 48 days. Do I still need to file 1040 for 2013? Also Do I need to report foreign bank and financial accounts?
Permanent residents of the U.S. follow the same rules that apply to U.S. citizens for tax purposes. Total duration of stay in the U.S. in 2013, and the fact that for part of the year you did not have permanent resident status, might affect how some non-U.S. income and non-U.S. taxation is treated on your 2013 income tax return, but you will need to file a tax return in the U.S. for 2013.
You file 1040 as a US resident for the whole year, if you had a green card any time during that year. This is called "the Green Card test" for residency.
That means that regardless of where you live, you file as US tax resident, and pay taxes on your worldwide income. It also means you're required to file the FBAR and FATCA forms and other forms and taxes related to the foreign income and holdings.
As mentioned in the comments, first/last year of residency may be split into dual-status years. You should check, depending on your own specific situation, if this option is available for you, and if it is - whether it is advantageous over claiming residency for the whole year.
Note, that if you were present in the US in the recent years, the fact that you've been in the US only 48 days this year may not preclude you from being considered a tax resident regardless of the green card status date.
Not filing your tax returns properly may lead to revocation of your green card at any time. Filing a "NR" tax return (non-resident) or claiming bona-fide foreign residency on your tax return will almost certainly lead to revocation of your green card by the USCIS.
As any US citizen/resident, you can exclude portions of your foreign income based on the days count or use form 1116 to credit foreign taxes paid.