I urinate every 10 to 20 minutes, will that cause dehydration?

Seek MD advice. If frequent urination is because of a defect in your kidneys ability to retain salt and/or water, then you might become dehydrated or develop a severe electrolyte abnormality. Uncontrolled diabetes can also cause frequent urination and dehydration. Excessive water ingestion as well as bladder obstruction or infection can cause frequent urination. You need to seek medical consultation promptly.
See physician. Urinating that frequently is unusual. You should see a physician to have an evaluation of your symptoms. There are potential issues other than just dehydration that could be involved.