B4 I got a jailbreaken downloaded paid apps and why it failed to sync to my phone even though I hv jailbreak my ios 6.1?

I hv iphone 5 Jb, after sync everything to itunes then i straight update from 6.1 to 6.1.2, i will lose all the "apps" right?

(1) Anyone's FB apps on ios 6.1.2 always crash and pops out to the home screen? crash frequently on mine

(2) software update on phone just keep loading but didn't pops out the content ask you to update (since now edi on 6.1.4)...my phone din show update since 6.1.2

My phone was JB iphone5 6.1.2

After i connect facebook to cydia, manage account i link to fb too, and update everything on cydia, install fb page update...the prob solve, it won't crash anymore, don't know which option fix the crash..