When you are using the word and phrase like 'little' or 'a little' adverbally (like below), how inserting an object make the sentence different?

1. Please open a little. (Looks to be fine, seems to be from a positive-polarity view point)

2. Please open little. (Looks fine too, seems to be from a negative-polarity view point)

Then, let me put a direct object, which, in this situation, is the 'window', to them.

3. Please open the window a little (bit). (Looks good and a positive-polarity view seems to prevail here too.)

4. Please open the window little. (Doesn't look good and doesn't seem like a correct sentence.)

My Q: A dictionary of mine seems to indicate 'a little' and 'little' as adjectives and adverbs both, then shouldn't all 4 sentences be valid since that word and phrase are functioning as adverbs in all 4 instances?
"Please open a little." seems fine because the speaker is referring to you understood (imperative sentence) and wanted you to open up a little (referring to your emotions/thoughts).