Hello,
Thank you for posting in the HP Support forum.
Yes, it is safe to delete these as long as you install your own copy of Windows 7 (or any other Windows, or OS).
These partitions HP docs and DOS are for the free operating system (OS) that your PC came with - FreeDOS:
>> https://en.wikipedia.org/wiki/FreeDOS
This OS is practically useless nowadays - you cannot use not even 50% of your PCs features with it. FreeDOS (or similar) is installed so that you can actually see your computer boots but you need to install Windows or Linux on your PC to make it run, make it usable. So, yes, delete all partitions and install the OS of your choice
Once Windows is installed, you can get its drivers from >> http://support.hp.com/us-en/drivers/selfservice/HP-14-Notebook-PC-series/7771392/model/8189730
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*** HP employee *** I express personal opinion only *** Joined the Community in 2013