What are the problems/risks of a fast heart rate for your heart?

Depends on rate: In adults: heart rates of 90-110 are harmless and may be appropriate depending on circumstances. Persistent hr of >120 can cause weakened heart muscle leading to heart failure ("tachycardia mediated cardiomyopathy"). Hr >150 often causes dizziness and breathlessness. Hr >200 often causes dizziness or passing out . Hr> 250 causes shock and leads to death. None of this applies to infants/children.

Varies.: High resting heart rates 100+bpm may be a sign of illness and are associated with cardiomyopathy when sustained for very long periods. High exercise induced heart rates 130+bpm may be conditioning and beneficial. Extremely high rates such as seen with some tachycardias 220+ may be suddenly fatal as forward flow fails due to inadequate pump fill.