AlexH - that is incorrect. The Admin site has nothing to do with the fields you see when logging a defect.
anjuman - have you spent time going through the user's guide? If not, please do and focus on the workflow coding section. It will inform you on how to enable/disable and make visible/invisible fields on the screen. Once you have gone through that exercise, if you have any specific question please come back and post it.
Insanity: doing the same thing over and over again and expecting different results
You wont be able to remove the system fields, although you will be able adjust whether these fields are visible, read only, etc.. This is a function carried out through project customization. It is not necessary to be in the admin site.
You will be able to change the properties of system fields for new and existing defects. Refer to the document library for more info, specifically - Administrator's Guide>Workflow Customization.
As for existant defects, as you are not really removing fields there will be no problems there. You maybe should check that the fields you want to change the properties for are not used in personalised reports, whilst the reports will still work, the data maybe different from that expected.