Can I replace the missing velvet lining?

Replacing degraded lining is standard practice. Box restorers use modern silk velvet to recreate the original padded compartments. Try to match the original colour if remnants survive under the trays. Deep blues and dark greens were standard for the period. Keep any original brass hinges or pins during the process. They fit the existing recesses better than modern replacements.

I have noticed that the brass strips on the corners of my box are lifting slightly away from the wood, is this something that needs fixing immediately?

Lifted brass edging happens as the wooden carcase shrinks over time. The metal stays the same length while the timber contracts, forcing the pins outward. Securing it prevents further damage. Loose brass catches on clothing and bends easily. Once bent, the strips are difficult to flatten back into their original shape.

How do I unstick a jammed drawer?

Damp weather swells secondary woods. Wait for a dry spell. Don't force a tool into the gap. You'll damage the veneer.

The lock on the main compartment seems to be locked but I do not have the original key, can a normal locksmith open it for me?

High-security nineteenth-century locks require specialist knowledge. A standard high street locksmith may drill the mechanism and ruin the lock plate. Seek out an antique furniture restorer. They keep stocks of antique keys and can carefully pick the lock or file a new key to fit the levers.