There are always some files that a user must create. If he opens an editor or a word processor, he reads and creates or updates files.
You probably mean in directories for which he is not an owner. Well, this is managed by the permissions for directories and these permissions may extend to files. /tmp is always kept with universal access.
Regarding Quotas, There are standard ways to do this. You must consider if quotas are global or limited to individual users. Tell us more details and we will see about appropriate responses.