pensar en = to think about. Pienso en mi familia todos los dias. Your notes flag this preposition explicitly.

pensar que = to think that, when an opinion follows. Pienso que es una cancion romantica.

The trap: English drops "that" and Spanish cannot. Pienso es romantica is wrong; it needs que.

When the object is a person, Spanish inserts a. Your notes give the rule on odiar: Odio a personas maleducadas.

Same with conocer a tu familia, ver a Maria, querer a alguien.

The trap: no a when the object is a thing. Odio el trafico, veo la television.

pensar: pienso, piensas, piensa, pensamos, pensais, piensan.

sentir: siento, sientes, siente, sentimos, sentis, sienten.

Same family: querer, preferir, empezar, cerrar, entender, despertarse.

The trap: creer looks like it belongs and does not. It is fully regular: creo, crees, cree, creemos, creeis, creen.