Not native, but it can be: https://yourdailygerman.com/2014/05/09/meaning-ansehen/
Both are possible -- German also uses the present tense to indicate intentions for the future.
mir means something like "for my benefit" here.
Sort of the difference between "I will cast my eyes on it" (ich werde es ansehen) and "I will look at it in order to form an impression or an opinion in my mind" (ich werde es mir ansehen).
Future tense is often used to express a probability, an assumption, an intention, or a doubt: Mein Freund wird mich hoffentlich nicht im Stich lassen. Der Bus wird vielleicht Verspätung haben. Ich werde mich bessern. Wir werden sehen.
In this case, an action is being expressed, and for a future action, the present tense is used.
"I will look it later" doesn't work in English. You need to say "I will look at it later." This page explains: http://www.macmillandictionary.com/us/dictionary/american/look-at
[US English native speaker]
"I'll see to it" involves a different phrasal verb. It doesn't mean "I'll look at it," but rather "I'll take care of it" or "I'll make sure it gets done." Here are a couple of explanations/definitions: