Re: cover question
The principal function of the cover is to protect the coils physically and to screen them against electromagnetic interference.
A side effect of this is that the cover, the same as any electrical screening, has a capacitance value which affects the treble content. The degree to which this is noticeable will depend on the way in which the pickup is wired internally.
A tertiary effect occurs when a cover is made of a steel based material rather than a non-magnetic material such as brass. A steel cover is less magnetically transparent than a brass cover will affect the density and dispersal of the pickup's field.
The small airspace contained within a covered pickup can vibrate at high gain, causing fluctuations in the pickup's capacitance owing to microscopic changes in air density, increasing microphonic effects such as squeal. At low gain however this can create unique overtones which some see as desirable.
Chacun á son goût, I say.