Will the shelves hold heavy books?

Solid pine or oak shelving from the Georgian period handles significant weight without bowing. They were built for dense leather-bound folios. Check the wooden support brackets on the inside. If the sawtooth supports remain intact and the wood is thick, they will easily take a full load of modern hardbacks.

My house has fairly low ceilings in the living room, so do these tall cabinets usually come apart for moving into smaller modern properties?

Most tall bookcases split into at least two sections. The glazed upper half lifts away from the deeper base cabinet. Large breakfronts often dismantle further. The cornice lifts off, and the upper and lower sections can split into three vertical bays. Check the sides of the carcase for joining screws.

Can you replace broken glass panes?

Yes. Glaziers can cut replacement glass to fit the original astragal bars. Old crown glass has a distinct wobble. Modern float glass looks flat and lifeless by comparison.

I noticed the lower doors on some of these cabinets have solid wood panels while others seem to have wire mesh inserts, why is this?

Solid wooden panels provided hidden storage. Cabinets housed ledgers, loose papers and boxes that owners preferred to keep out of sight. Wire mesh allowed air to circulate around the books. Brass grilles often feature a pleated fabric backing to keep dust off the contents. Regional trends also played a part. Certain provincial makers preferred solid timber doors throughout the century.