The formality is decided by speech styles. '이해(가) 가다' and '이해하다' just have slight different meanings. For example, "이해(가) 가요." is less formal than "이해(가) 갑니다." Or "이해해요." is less formal than "이해합니다." However, "이해(가) 가요." and "이해해요." are both polite forms.

In my case, I use 이해하다, when I understand something in my own. Maybe common meaning of 'understand' I ask the question to my teacher and my teacher teaches me how to solve this problem, the I say to my teacher "나는 이해했어요" I use 이해가다. It is similar, but little bit different. This word is used in the other people's case. When I heard the conflict between A and B. I heard the A's situation and I understand A's situation, then I say "A의 상황이 이해간다." 이해하다. I understand some situation that is related with my case. 이해가다. I understand some situation that is related with the other people's case. ex) 나는 그의 마음을 이해한다. I understand his mind in my words. 나는 그의 마음이 이해간다. I understand his mind in his case that I think I am in his mind. 여러분 이해했습니까? / 너 이해했어? Do you understand this?(The talker want to know the people understand) 여러분 이해가 갑니까? /너 이해가 가?You understand this?(The talker consider the people's considering) I think '너 이해했어?' is more positive and polite in this case

Hi, they are not less formal than the other. More like the nuance and expressions are different. You might want to read this webpage for reference: https://canaderuraee.wordpress.com/2014/05/14/lets-study-hanja-to-understand/ Hope this helps!