As to if an OS upgrade will solve your problems, it depends on the root cause of the problems.
An upgrade to XP Pro will solve most problems related to corrupt Windows files.
An upgrade is not apt to repair problems in the Windows registry.
The biggest difference between XP Home and Pro is that XP Pro has more advanced networking capabilities.
If this PC is used as a stand alone home system, or the home network is primarily used to share a network connection, save the money and find a different way to correct the problem.
I would start with a registry cleaner.
While my personal choice is Fix-It from V-Com, Norton Win Doctor does a good job too.
There are 2 good registry cleaners that you can download as 30 day trial versions.
Registry Fixer from www.rosecitysoftware.com
And System Mechanic from Ilio Systems.
As to your other upgrade questions:
When you upgrade with XP Pro, it will keep only supported applications.
Since the system has XP Home installed, most of the applications should be fully supported.
As to files and user settings like bookmarks, those will be left intact. So long as nothing goes wrong.
It is ALWAYS best practice to back up critical files prior to any major software or hardware installation.
If this were a system that I was responsible for, and it is a home PC that is not networked, I would:
Back up the user files.
Collect logon and password information.
Get the install disks for the software the user actually uses.
Then, format the hard drive and start over with a clean installation of XP.
Chas