Is it allowed for a person to exaggerate some things on their resume being that it is a widespread and common practice?

An example would be adding a few months of experience to fit as “6 months of work”, or if a person is not sure from when they worked at a place they put an automatic 1 year or an automatic 6 months as their experience.

Making a false statement on the resume would be haram. However, one an be creative and state one’s experience in a way that is more effective. Now if you technically have done 6 months of work that’s related to your field (even though it’s not directly about the job you are seeking), then you can list that since it’s not a false statement. So the key is not to give a false statement, but you can be creative in making your resume more impressive.