Wouldn't that make things worse? Those applications usually expect to be able to make these calls. So now, instead of lagging once in a while when the home base is having troubles, it will lag all the time.
Not necessarily. The lag may be waiting for the remote server to respond to a request, and the app may move on quickly if it can't open a connection at all. It's not totally uncommon to work totally offline (e.g. on an airplane), so there's a decent chance the test that scenario.
Which would take longer. I haven't tried though
If you are getting timeouts then the folks who set up the firewall hate you.