Activities are stored in the table called TASK
Security Profiles are stored in the table called PROFILE (field of scope_type defines if it is Global(ST_Global) or Project(ST_Project))
If you are on 8.3 then you would also need to backup your background job user and possibly extended schema user if you are using EPPM.
This is the command I issue to do a backup (i'm assuming an Oracle database given you are referring to admuser as this account doesn't exist for SQL).
exp system/<system-password>@<SID> file=C:\backup-file-name.dmp owner=(admuser,privuser,pubuser,bgjobuser,pxrptuser) log=C:\log-file-name.log grants=y constraints=y statistics=none