The jeweler will charge a small nominal fee to reattach the stone back on your bracelet, unless they sold it to you.
You might be able to pry the stone out of the setting. A better idea would be to take the ring to a jeweler and ask the jeweler to remove the stone in a way that will best preserve the setting.
A diamond is 'worth' what someone will pay you for it. Take your stone to a jeweler and ask the jeweler to buy it. Then ask the jeweler to show you a comparable stone and ask how much it would cost you to purchase the stone. In the grande scheme, any diamond is valued by its cut, colour, clarity and carat weight.
To determine if a diamond is real, you can perform tests such as the fog test (breathe on the stone and see if the fog dissipates quickly) or the water test (drop the stone into water to see if it sinks). You can also seek professional help from a jeweler who can accurately assess the authenticity of the diamond using specialized tools.
Your local jeweler can help you determine whether or not the crystal coloured stone you have is a diamond or not.
You can test it wouth a touch stone.
Take your diamond to a jeweler who can test the stone to confirm that it is or is not a diamond.
Take your diamond to a local jeweler whom you trust, and work with the jeweler to set the stone in the metal. The jeweler will charge you for workmanship and for raw materials required to accomplish the finished product that you commission.
Take the raw stone to a jeweler who can apply a probe to the stone to determine whether or not it could be an uncut diamond.
Many jewelers are willing to clean diamonds at no cost. Best practices dictate that you work with a jeweler that you know and trust. Be certain, however, that in this process, you never lose sight of the diamond, to prevent its being swapped out for a lesser value stone in the cleaning process. Some unscrupulous jewelers have been known to practice this deception.
Carats describe the weight of a stone. A jeweler can show you the scale used for this purpose.
You can determine if a stone is a diamond by conducting a visual inspection to check for specific characteristics like clarity, color, cut, and carat weight. Additionally, you could confirm its authenticity by taking the stone to a professional jeweler or gemologist who can perform tests such as a thermal conductivity test or a diamond tester.