In "package," the free morpheme is definitely "pack." "Pack-" is the word-unit that can stand alone, which makes it the free morpheme. "-age" is a morpheme, too (e.g. it's also used in "baggage," "luggage," usage," and a large number of abstract nouns), but it can't stand alone, making it a bound derivational morphone.
"Carelessly" has three morphemes. "Care-" is a free mropheme. "-less" is a bound derivational morpheme, because it can't stand alone and is used to make new words (adding "-less" usually changes a noun to an oppostite adjective). "-ly" is also a bound derivational morpheme, I believe, but I'm not entirely sure. If "-ly" is seen as a grammatical marker, it might more accurately called an inflectional morpheme.
Derivational morphemes are things like "un-" (as in "unlikely") and "-ous" (as in "virtuous"). Inflectional morphemes are a much smaller group of short grammatical markers. They include the standard noun plural marker (the "-s" in "cats"), the standard past tense of verbs marker (the "-d" in "liked"), and perhaps the standard comparative and superlative adjective markers ("-er" and "-est").