Is it possible to get stains around ceramic braces where the glue is? will the glue and stains come off when braces are removed?

Yes: The glue is a resin, and as such it can get stained. As a general rule, most stains come off once the braces are removed, the resin used to bond the braces is removed and the teeth polished. Just be careful and maintain good oral hygiene. In some cases where stains remain, other procedures can be done to completely remove them or minimize their appearance.

It is possible: In addition, it is also possible to get cavities, especially if your oral hygiene is not terrific. Brush well and follow your orthodontist's instructions. The stains should come off when the brackets are removed.

Stain/scar: Stains are extrinsic, and will clean off easily during or after braces with a professional cleaning. If braces are not kept clean and bacteria allowed to collect next to the braces, or if seal is damaged from eating hard/sticky/chewy foods, teeth can become permanently damaged, intrinsically scarred, requiring restorations. Ask both your Orthodontist and your Dentist to review your status.

Yes: Usually, the ceramic braces do not stain, however the glue does. Ask your orthodontist (or dentist) to please remove the excess glue. The glue should be entirely removed when your braces come off.

Yes and yes: Stains can be caused by you eating and/or drinking things that stain your teeth. In these cases, the tooth under the brace is protected from these elements and may stay whiter than the surrounding area (the glue does not stain, its what you are eating and drinking). however there are treatments (e.g., MI paste) that can address this once the brackets come off

Braces: Generally yes I would assume that the stains would be able to be removed with the braces coming off. If the stain is the start of a cavity - that is unknown until the dentist or orthodontist checks on it - Have someone in dentistry check it out first.