A. sometimes sd card problem..can you swap it out, or at least format it or test it on a pc?
Just in case it applies to you, with this new phone's better storage, i don't move any apps to sd, they run faster when on phone anyhow.
B. does this 'also' occur on wifi?
C. have you tried temporarily disabling any security app-- lookout, avg, etc.?
If not, then I have the same issue.
1. Firstly, as to the network error-- "for me" it's only temporary, usually after not using the phone for awhile,...which i've attributed to the inherent nature of the new kernel / rom to conserve battery.
This holds true for any type of surfing too, and it's a tradeoff i willingly accept.
You can usually tell when the status bar 4G icon is missing, or is present but the arrows don't show activity either way.
Usually all it takes is retrying / refreshing any internet activity.
When that doesn't work, toggling airport mode(quickest way from the status bar) off & on does the trick.
Semi-related: when stuck at one of the lower network settings,
How to enable/disable 4G mode with Any Cut
comes in very handy.
2. As far as the apps themselves, an alternate market like appbrain or amazon usually does the trick.
FYI those two are incompatible-- they don't recognize an app installed from each other & will try to remove & reinstall, even when no update necessary.
Barring that, one can always try the clunky workaround of manually downloading the apk in question.
This highlights Android's dire need for a batch auto updater. (even appbrain's too slow & buggy)