Brand new update to the FaceBook app today. They added messaging and multi-photo posting. If those were the lacks you were lacking, maybe that will help.
EDIT: You may want to hold off on updating the FaceBook app. Some users are reporting problems logging in with it. Though I just tested it on my iPhone 5 and iPad 3 and experienced no issues.
As for Safari crashing, if you have not restarted your iPad lately, that might help.
Also, you can go into Settings > Safari and Clear Cookies and Data. You'll have to re-enter your password on all the sites that usually remember you, but it may help with the crashing. While you are there, look to see if you have Private Browsing turned on and/or are not accepting cookies. Either of these will keep FaceBook from remembering your password between sessions, even if you check the remember me box on the site
Normal settings are Private Browsing OFF, and cookies accepted from visited.
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When you have problems with an app it's a good idea to clear it from RAM.
Close/Clear the app: With the problem app closed, double tap on the Home button to get the multitask bar. Tap and hold on any icon in the bar until they jiggle, then tap the minus sign on the problem app. This will remove it from RAM and insure a clean start the next time you launch the app.
If that does not work try a restart,
Restart: Hold down the power button until the power off slider appears. Slide it off. When the iPad finishes shutting down, hold down the power button again until the Apple logo appears. Apple recommends you restart the iPad at least once a month.
and then a reset if that does not work.
Reset: Hold down the power and home buttons until the Apple logo appears. The iPad will reboot. This usually takes a bit longer than a restart. takes a bit longer than a restart.