Fetch Customer Profile from Line Items
The rule isn't running because of my fault in the parameter settings the parameter commerce_customer is giving problems, I get an error that says: &quot;Missing configuration for parameter commerce_customer&quot;.
How can I get to this information in my component?

It looks like you have a mismatch in the variables of your rules component (which has 3 of them) and the rule which invokes that rules component (which only passes a value for the first variable selected_line_item).
Here is what I suggest you try to get the 2 remaining variables for your rules component fixed:

commerce_order: in your rule (which invokes the rules component), add the value of it as your 2nd variable (to actually pass that value to your rules component). For sure you have a token available to actually pass it (= commerce-order), since your rule already refers to commerce-order:commerce-line-items also (which you would not be able to do if you wouldn't have commerce-order).

commerce_customer: just remove (delete) that as your 3rd variable in your rules component. It seems you don't need to &quot;pass&quot; that as a variable, as per the (2nd) entity_fetch included in your rules component. Whereas this (2nd) entity_fetch will return you that entity_fetched (BTW, a terribly bad name IMO, consider changing that to something more meaningful like fetched_user, or even better fetched_customer).
Whatever you end up using (i.e. entity_fetched, fetched_user, or fetched_customer) that's what you can then use within the body of your eMail (any of the tokens related to it).