Ich arbeite hier zwischen 01. Februar und 15. März.
Ich bleibe hier bis 22. April.
Ich bin von 05. bis 12. Mai in Mailand.
Do these sentences need articles for dates, or are they fine as they are?
No, with days and month you'd need to use an article. So it would be:
But not with times:
You can find an overview of the use of the different temporal prepositions here
As a native speaker, I would use articles.
The first sentence could work without articles, if you read it as 01. = "erstem" und 15. = "fünfzehntem".
Keep in mind, that I don't know if there is any rule, it just sounds right for me.