We can experience health problem due to dental problem like gingivitis?

Possibly: There has been some research that supports a link between periodontal disease and cardiovascular disease. In addition periodontal disease can disrupt diabetic control for people with diabetes.

Yes, definitely: Poor oral health can definitely lead to other health problems. Gingivitis and periodontitis create open areas for infection to enter the body. The mouth is the area where everything enters your body including food, water, air, and bad things such as bacteria and viruses. Optimal oral health reduces infection and sickness throughout the body.

Yes there is a link: Gingivitis is an infection in a part of your body. Would anyone be surprised if we said that in infection in your toe can affect other health problems? The mouth is connected to your body too. Specifically, there is a relationship between gum health and diabetes and some kind of relationship with oral health and cardiovascular disease. There are probably others we just don't know about yet.