袋: bag, sack, pouch, pocket, handbag, plastic bag, etc.; 包: bag, sack, packet, wrapper, backpack

Both of them can be a noun.

Update:

As classifiers/quantifiers, They can be synonyms for soft rectangular sacks that serve as a product's packet, e.g. rice sacks. But they also differ in many places. The intuitive impression in brief: 包 is more of “wrapper, pack, packet”; 袋 is more of “pouch, pocket” (usually made with soft material and a unsealable/sealable opening, e.g. plastic bags, paper bags, rice bags).

They're interchangeable classifiers for bags.

Reported

How about "which one"?

Yes, 那 Nā/ㄋㄚ and 哪 Nǎ/ㄋㄚˇ both look and sound quite similar, which doesn't help

Both correct. Re “那个包是你的？”:

• I think a better (and more literal) interpretation/translation should be “That bag is yours?” (please note the question mark & your intonation)
• Conversely, “Is that bag yours?” should be “那个包是你的‹吗›？”
• Yes, I mean the nuance is roughly the same in both Chinese and English. And of course a proper intonation & context allow you to convey the same meaning no matter you're saying “那个包是你的？” or “那个包是你的吗？”. However, the listener may not think so, especially when the sentence is written down instead of spoken out. Now whether to include 吗 at the end is up to you.
• Context & intonation bring a lot of confusion to the discussion. Honestly, I don't know how Duolingo should solve this problem. There is too much inconsistency in the course.