The 'd' is capitalised because the person writing the sentence has made a mistake. You were correct to notice that something was amiss there. Is the only context you have? Without further context, it is impossible to say exactly what it means.

"I got it off" means "I got it from" and applies to objects/things. It's casual language. "Where did you get the $10?" "I got it off my dad." There's a feeling that maybe he didn't really want to give it to you, but you convinced him to.

It is not capitalized because it's using a common noun ("a dad"), not a proper one ("Dad"). When you are using the word "Dad" to refer to a specific person, it's standing in place of their name, and thus, like their name, would be capitalized. There is a common phrase, "I got it from my dad" means I have similar characteristics. For example, I got my musical talent from my dad or I got my looks from my dad is common. However, I got it "off" my dad is not common. Hope this helps!

It should be "I got it off of my dad." Or "I got it from my dad." We are bad about leaving some words out.