For the first sentence here cf. John Philoponus, Commentaries on Aristotle's de anima 273.8-9 Hayduck.
[1] Aristotle distinguished four kinds of causes or explanations (Posterior Analytics 94a21-3; Physics 194b24-33 = Metaphysics 1013a24-33; Metaphysics 983a27-32; On the generation of animals 715a4-7). The four named here correspond to his, but do not indicate the exact names he used in describing the four kinds of cause.
[2] Or "what is productive of what is produced" (see Aristotle, Physics 194b31). Consider a typical example, the causes of a house: bricks and planks (matter); the layout or blueprint (form); sheltering goods and people (end); the architect and builders (maker). The subsequent distinctions are not Aristotelian; they are probably Stoic (see Hankinson, p. 245f.).
[3] Antecedent causes precede in time their effects; the removal of an antecedent cause does not remove the effect. The distinction has major significance in Hellenistic (especially Stoic) discussions of fate and determinism. See Hankinson, pp. 244-247. Galen wrote a treatise On Antecedent Causes. On Stoic forms of causality see M. Frede (1980), 217-249.
[4] Auxiliary causes contribute to an effect, but do not bring it about on their own. Sextus Empiricus gives as an example the case of two men lifting a heavy weight with difficulty, and so a third (an auxiliary cause) lightens it (PH 3.15).
[5] Sextus Empiricus (PH 3.15) gives a different threefold division: sunektika/ (immediate or containing), sunai/tia (cooperative or associate), and sunerga/ (auxiliary). The present term telika/ may refer to the first of these, i.e. the immediate or containing cause. Alternatively it might refer to the "perfect" (perfectae) kind of cause also mentioned by Cicero, On Fate 41, in connection with "principal" causes in opposition to auxiliary causes.