@Prasenna Kannan , Please find the answers to your questions below.
1) Dev\Test Pricing is applicable only to VS Professional and VS Enterprise subscribers and not VS Community Edition? From this link, I see that https://visualstudio.microsoft.com/vs/pricing/ only VS Professional and Enterprise are eligible for Dev\Test pricing.
That's correct. VS Community is a free edition which does not come with any subscription benefits.
2) Can the existing VM's which are developer VM's and in Pay as you go subscription be shifted to Dev\Test pricing plans? How?
Once you have your DevTest enabled Azure subscription, you can move your existing VMs in current subscription to that new subscription by following this guide. Note that you should also include the dependent resources for the VMs.
3) There are 3 options available for Dev\Test pricing. 1) Individual 2) Enterprise Agreement (private business requires 500 users and devices, public 250 users), 3) Teams. We have less than 10 developers. In our case, the option 3 is the option left to switch to Dev\Test pricing plan, correct?
That's correct. You can go for Teams Pay-As-You-Go
Also, to manage VMs for your team more efficiently, I would suggest you to look at the Azure DevTest Labs service.