What tests do you suggest for the evaluation of Dementia and Alzheimer's Disease?

Alzheimer’s disease (AD) has been associated with oxidative stress, inflammation, and impaired glucose regulation.

You definitely want to assess for oxidative stress, antioxidant status, and GGT which facilitates glutathione metabolism.

Albumin
Bilirubin
Cholesterol, total, and LDL
Copper, ceruloplasmin
Ferritin
Globulin, total
Glucose regulation markers
Gamma Glutamyl Transferase (GGT)
Lymphocytes
Malondialdehyde
Platelets
Uric acid
Vitamins A, C, E, alpha and beta-carotene

Schrag, M et al. “Oxidative stress in blood in Alzheimer's disease and mild cognitive impairment: a meta-analysis.” Neurobiology of disease vol. 59 (2013): 100-10. doi:10.1016/j.nbd.2013.07.005

Evaluation of inflammation would be prudent as well given its association with Alzheimer’s and should include the basics not already included in the above recommendation:

Erythrocyte sedimentation rate (ESR)
Ferritin
Fibrinogen
Homocysteine
hs-CRP, CRP (though CRP can increase, decrease, or be unchanged in AD)
LDH
TNF-alpha
Vitamin D

Additional research suggests an association between mild cognitive impairment/Alzheimer’s and

apoE
BNP
Cortisol
CRP
IL-3
Pancreatic polypeptide

Hu, William T et al. “Plasma multianalyte profiling in mild cognitive impairment and Alzheimer disease.” Neurology vol. 79,9 (2012): 897-905. doi:10.1212/WNL.0b013e318266fa70

Anemia is also a common finding in AD so be sure to assess the following:

Ferritin (though may be high in AD due to tissue accumulation)
Iron, serum
Hematocrit
Hemoglobin
Packed cell volume (PCV)
Red blood cell folate
Transferrin, transferrin saturation

Faux, N G et al. “An anemia of Alzheimer's disease.” Molecular psychiatry vol. 19,11 (2014): 1227-34. doi:10.1038/mp.2013.178

An anti-inflammatory diet high in antioxidants and moderate in carbohydrates can be beneficial. Curcumin may be especially beneficial (black pepper/bioperine may increase bioavailability). Medium-chain triglycerides and ketone monoesters may also be beneficial supplements as they provide energy to the brain.

Newport, Mary T et al. “A new way to produce hyperketonemia: use of ketone ester in a case of Alzheimer's disease.” Alzheimer's & dementia : the journal of the Alzheimer's Association vol. 11,1 (2015): 99-103. doi:10.1016/j.jalz.2014.01.006

Reddy, P Hemachandra et al. “Protective Effects of Indian Spice Curcumin Against Amyloid-β in Alzheimer's Disease.” Journal of Alzheimer's disease : JAD vol. 61,3 (2018): 843-866. doi:10.3233/JAD-170512

Also, researchers note a strong association between Alzheimer’s and herpes simplex virus type 1 (HSV1) and associated testing may be prudent.

Itzhaki, Ruth F. “Corroboration of a Major Role for Herpes Simplex Virus Type 1 in Alzheimer's Disease.” Frontiers in aging neuroscience vol. 10 324. 19 Oct. 2018, doi:10.3389/fnagi.2018.00324

Additional References

Faux, N G et al. “An anemia of Alzheimer's disease.” Molecular psychiatry vol. 19,11 (2014): 1227-34. doi:10.1038/mp.2013.178

Hu, William T et al. “Plasma multianalyte profiling in mild cognitive impairment and Alzheimer disease.” Neurology vol. 79,9 (2012): 897-905. doi:10.1212/WNL.0b013e318266fa70

Itzhaki, Ruth F. “Corroboration of a Major Role for Herpes Simplex Virus Type 1 in Alzheimer's Disease.” Frontiers in aging neuroscience vol. 10 324. 19 Oct. 2018, doi:10.3389/fnagi.2018.00324

Newport, Mary T et al. “A new way to produce hyperketonemia: use of ketone ester in a case of Alzheimer's disease.” Alzheimer's & dementia : the journal of the Alzheimer's Association vol. 11,1 (2015): 99-103. doi:10.1016/j.jalz.2014.01.006

Reddy, P Hemachandra et al. “Protective Effects of Indian Spice Curcumin Against Amyloid-β in Alzheimer's Disease.” Journal of Alzheimer's disease : JAD vol. 61,3 (2018): 843-866. doi:10.3233/JAD-170512

Schrag, M et al. “Oxidative stress in blood in Alzheimer's disease and mild cognitive impairment: a meta-analysis.” Neurobiology of disease vol. 59 (2013): 100-10. doi:10.1016/j.nbd.2013.07.005