Care and Keeping
Nothing here needs much from you. Most of these objects have already survived a century or more of somebody else's household, and the most common way to damage one now is to try to improve it.
Silver and plate
Leave the tarnish.
Every polish removes a thin layer of metal and leaves fine scratches, so over decades marks soften and engraving loses its edge. If you do polish, use a wadding or a soft cloth product made for silver, work gently, and stay off the hallmarks.
Silver plate is even worse to polish: there is only so much silver on top of the base metal and once it is gone it is gone. The Canadian Conservation Institute's note on the care of silver covers this properly.
Hair, textiles and paper
Light is the enemy.
Keep hairwork, silk ribbon, antique books, mourning cards and photographs out of direct sun and away from a window that gets afternoon glare. Fading is not reversible.
Hair under glass wants a stable, dry room. If the glass ever loosens in its bezel, stop handling it and get it re-sealed by somebody who does this work.
Jet, vulcanite and black glass
Do not soak it.
Whitby jet is fossilised wood, so it is light and warm against the skin, and chips easily. Wipe with a barely damp cloth and dry it straight away.
Vulcanite is hardened rubber and it browns and dulls with sunlight, which is often how you tell it from jet in the first place. Black glass, sold in the period as French jet, is heavier and cold to the touch and it chips easily too.
Living with it
Wearing it
You can. People did. Take it off before washing up, sleeping or swimming, and check the clasp against a table before you trust it to a coat.
Storage
Separate compartments or soft pouches so pieces do not knock each other. Somewhere with a steady temperature, which usually rules out attics, basements and the top of a radiator. Silica gel helps in a damp house and needs replacing when it stops working.
When it needs a conservator
Flaking enamel, a split in a hair panel, corrosion that looks powdery rather than dark, or any repair that would need heat. Do not attempt those at home. The Institute of Conservation keeps a public directory, and the American Institute for Conservation publishes free guidance for owners.
Sources
The notes above lean on these three, all free to read.