Yes the 'I'm' is from the verb 'to be'.
'I'm going to' is the phrase we use to talk about future intentions, or plans which are not yet fixed. It is very common to use 'I'm going to' to talk about the future. Here are some more examples:
'I'm going to visit my friend tomorrow' (a plan, but maybe I am not sure what time yet, the plan is not fixed)
'I'm going to study English today' (again this is a plan, but maybe you are not sure when, but you know you are going to do it)
We use 'will' to talk about 3 things mainly
- spontaneous decisions: 'I think I will get myself a coffee'
- promises ad offers: 'I will help you with this answer'
- predictions: 'I think artificial intelligence will take over the world'
This diagram might help with future tenses: http://englishtenses.eu/find-your-tensefuture/