The set of "all the conjugated forms from just one stem" is the stem's paradigm or declension; another term is the set of "all the inflected forms of a stem."
A paradigm is the inflected forms of a verb. For the English verb 'walk', the paradigm consists of 'walk', 'walks', 'walking', and 'walked'. For the verb 'run', the paradigm would be 'run', 'ran', and 'running'.
Some languages (Vietnamese, for example) have only one form of a verb, while others (Spanish, Finnish...) have many inflected forms.
Nouns and adjectives may also have multiple inflected forms, but these are usually referred to as their declensions. English noun declensions are pretty simple: 'book' and 'books', for example. Other languages (famously German) have more forms in their declensions, and some languages still more (Finnish, Russian).
A general term for the forms of a paradigm or declension is "inflected forms."
The prefixes you say you are not interested in are generally considered to be derivational morphology, not inflectional. But know that in other languages (Mayan or Nahuatl, for example), some prefixes are inflectional.
Linguists do not use the term 'cognate' in the sense of the para you quote. Rather, cognates are pairs (or triples...) of words in different languages that have a common source in some ancestral language. English 'hound' and German 'Hund' ("dog") are cognates due to both languages descending from a common ancestor thousands of years ago.
Similar to cognates are loanwords, which are pairs etc. of words in different languages, but where one language borrowed the word from another. "Fiance" (and "fiancé") is a loanword from French into English. Depending on how long ago a word was borrowed, and whether the two languages from that time are attested (i.e. know from written documents), it may not be possible to determine whether a pair of similar words are cognate or loans.
I'm not sure what the paragraph you quote is getting at. I think it's referring to derived forms, not (only) to inflected forms. 'Intention' is a noun derived from 'intend', 'intending' is an inflected form of the verb 'intend', and 'intentionally' is an adverb derived from the noun 'intention'. If you wanted to refer to both derived and inflected forms, one way would be to simply say "derived and inflected forms", another might be "morphologically related forms."
In general, inflected forms of a word have a meaning which is obviously and clearly relatable to the stem. This is not always true of derived forms, for example "deliverance" cannot be used in all the senses that "deliver" can: we don't talk about the "deliverance of a package".
Beware also that there are similar words which appear to be derived from some root, but where the different words have no meaning in common, nor can any real meaning be assigned to the roots or affixes, for example: prefer, confer, defer, refer, infer. It's not clear linguistically whether these are due to derivational morphology in the same way that intend, intention, intentionally are; for example, the root 'fer' is not a word of English. I would include your examples of 'suppose', 'depose, 'impose' etc. here; it's not at all clear that these have anything to do with the root 'pose' (which happens to be an English word).
