With my students, I'm happier calling this the "base form" of the verb and reserving "infinitive" for the "to+verb" construction. It is also sometimes called the "infinitive without 'to'".
The base form carries only lexical meaning because other parts of meaning (tense, person, aspect, modality, voice) are carried by the auxiliary verbs (do, be, have) or by modal verbs (will, shall, ought to, would, might, must, should...)
About "used to", I've only ever learnt (and taught) that this was used to talk about past states, habits or conditions which are now finished, in affirmative sentences ("I used to play in the park"). In negative and interrogative sentences, which require auxiliaries and therefore a "base form" of the lexical verb, you can express the "past habit" part with adverbs such as "never", "usually", "always" etc. ("I didn't usually play in the park", "I never played in the park", "Did you always play in the park"?). Oh, and textbooks generally stress the fact that this construction can only be used to speak about past states.
