Is it worth applying to job postings that are more than a month old,
especially for entry level jobs? Or is the time better spent applying
This is not an either/or situation. Do both. Applying doesn't take much time.
Apply for the "old" job opportunity, while continuing your search for others.
Is the logic correct, that if the exact ...
It'd be safest to presume that you need to have a submission by Jan 13 at 11:59 pm. If uploading to a web site, consider the factor of differing time zones. DO NOT do your submission at the last minute.
Or you could call, and ask.
There are many reasons why a job-posting might be "reposted" at a later date. (Maybe the original post did not yield any answers so the company tries on a different platform. Maybe some headhunter re-posts it regularly on as many platforms as possible to improve their chances. Maybe a second, identical position became available at the company in ...
The company has no obligation to even look at your application. So to be on the safe side, I'd make sure my application is in on the day before during business hours. If their office closes Thursday at 5pm, they might just throw away anything arriving later, unread. This may be unfair to anyone submitting their application later, but nothing you can do about ...
Emphasize the positive-- you really like the company-- and de-emphasize the fact that the current position isn't a perfect fit. I'd send an email something like this
I've really enjoyed getting to know the Foo Team and I'm looking
forward to my upcoming interview. During this process, I have come to
learn a lot about Company Name and ...