Is carbamazepine safe for alzheinmers patient who has been recently or seroquel (quetiapine) and is increasingly agitated?

It depends. There are older studies suggesting that Carbamazepine is helpful for agitation and aggression but it is less commonly used now because of drug-drug interactions and concerns about side effects. Seeing a geriatric psychiatrist can be very helpful at finding the right medicines.
Maybe. The other docs have answered most of what i would say about cbz. Just wanted to add that nuedexta, currently indicated for psuedobulbar affect, is now in efficacy studies for use in "agitation in the elderly" and does not carry the complicated interactions or need for blood work that cbz does, nor the risk of agranulocytosis or other medical complications. I would suggest talking to the doctor..
Likely. Both medications will need close monitoring, particularly when first started, for both effectiveness and for side effects. The tegretol will also need blood levels routinely.
Effective? I'm not aware of any good studies demonstrating the effectiveness of Carbamazepine for agitation in dementia, although there is alway the individual who will have a positive response regardless of what studies say! however, it does have a considerable side-effect profile and drug-drug interactions which makes it very difficult to use in most elderly patients and, generally, i don't use it.
Be careful. Carbamazepine has significant effects on liver metabolism and may even reduce the blood levels of seroquel (quetiapine). There are others to try first if not already.
Yes. The drug is used to help behavioral mood. It can be taken together with other anti-psychotic medication.
Yes. Generally tolerated if started at low dose and titrated upwards slowly by the doctor. Recommend checking Carbamazepine levels initially and on a routine basis to avoid toxicity. Carbamazepines belong to a group of medications known as antiepileptics that are used for seizure disorders, but have also been used for treating mood disturbance and dementia-related behaviors.
They interact. There is interaction between Carbamazepine and seroquel (quetiapine) if taken together...Psychomotor effects, efficacy issues (may verify with pharmacist). Carbamazepine is for prevention of seizures or to control neuropathic pain and bipolar disorder ( most common indications).
Probably. Carbamazepine is not a common medication in patients with ad. I am not sure what you'd use it for except in those who do have underlying seizure disorder. It is used in patients with bipolar disorder, however, ad patients are clearly different from bd, although, some features may overlap. Seroquel, (quetiapine) on the other hand, can be used for agitation, insomnia and depression.