I am working on getting my first job that uses my degree. I've had some related experience but it was short term contracts. Most of my searches start on Indeed. After finding a suitable job opening I try to find the company's website and apply directly through it (not sure if it increases my chances but someone gave me this tip). Often times I notice that the job posting dates do not match: Indeed could say it's 5 days old and another website with the identical posting could have 5 weeks.

1. 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 for another?
2. Is the logic correct, that if the exact same job opening is posted on another website (either the company's own or another job bank) then the older of the two posting dates is the right one?