Do native speakers pronounce all words with æ always in a similar way?
- For all these TRAP/BATH words, the very widespread GenAmE accent has /æ/ (top row), for all your examples.
- There are some American accents that do have what I think you're describing as /æ/ raising. This is most commonly found in the 'Northern Cities Vowel Shift' (note that this is an urban non-standard accent, and not widespread). It results in /æ/ sounding more like [ɛə] or [eə] or even [ɪə]. These are -higher-, where you seem to be hearing a lower vowel /a/ or /ə/. It could be that you are used to hearing an accent that has raising already and are noticing GenAmE speakers who do not have the raising.