1) I use "Ghost Commander", but it doesn't show the installed apps. You can browse the system and sdcard, but Android system structure is not like Windows (ie. not in Program Files, but in /data). It's possible to uninstall apps from "Market" application (Menu, "My downloads") or from Settings :
Sony Ericsson - Support - Phones - Detailed - Uninstallapplicationsfrommarket - Xperia? X10
If you install app, it doesn't show as widget (on normal Android, I know SEX is different, my siter also has SEX10), but will show in app list (called drawer), try to navigate there. This should be called "Application bar" and is accessible from homescreen. In worst case, you can add the application shortcut to homescreen (from the homescreen, tap applications bar, touch and hold an application until it appears on homescreen).
Good help can be found on Sony Ericsson web (just for Android 1.6, but most of it is valid for any Android version) :
Sony Ericsson - Support - Phones - Topic - Android16 - Xperia? X10
2) Application can be moved from Android 2.2. If you root the phone (be able to adjust system, load ROMs with new system and and void the varranty), you can install Android 2.2 or use Apps2SD application, which creates extra partition for applications on SDcard, According to Sony Ericsson there will be Android 2.3 update for SEX10 available soon (end of Q2 or early Q3 for non-operator customized phones). So if you're not familiar with rooting, want to be able to install official updates and want to keep warranty, I recommend to wait for this.