No, it's not impossible although Pocket IE has problems with a lot of sites. It sounds like one of your settings is wrong if you cannot reach any sites. Look in Settings, Connections, Connections to make changes, however, I don't use dialup so I'm not sure how these should be set. You can also get a different web browser - NetFront works at many more sites but it is not free.
Before trying to set that up, however, the
fix for your second problem is to disable the pass through option for web access. Look at this
website, item 14 under
Synchronization Errors for details. It looks like you have to make a choice between these two options (using the web from your Ax and not having it attempt to dial when you sync).