>Before I start linking computers together, I have couple of questions.
>
>Would I have any difficulty connecting Windows 7 and Windows 10 machines in peer to peer connection?

No.

>Also, does the fact that couple of computers are HOME versions and few f them are Professional version matter?

If you're contemplating linking more than 4 or 5 computers together I strongly recommend setting up a Windows domain. This requires an actual Windows server computer to act as an Active Directory/Domain Controller (DC). These days there are some file-sharing Network Attached Storage (NAS) devices which can act as Windows DCs despite not running Windows; they can be a lower-cost alternative to a true Windows server.

Any computer joining a domain must be Pro version or higher; if you want Home machines to join a domain you must upgrade them.

Most on-site peer-to-peer networks designate one computer as the master/"server", where shared files will be stored. For business-grade use it's a good idea to protect that computer with redundant hard drives (RAID1) and an uninterruptible power supply (UPS). You would also be doing this if you get a dedicated Windows server computer.

The bigger question is whether you want or need to set up an on-site peer-to-peer network at all. An alternative is business-class cloud storage which can be shared amongst multiple users. That way you don't have to mess with setting up an on-site peer-to-peer network, you just have to have a decent Internet connection.