how can i download nutanex AVH iso to test it?

If you would like to test Nutanix, you can use the Nutanix Community Edition, This gives you access to use the Nutanix products.

Otherwise, there is always the option to reach out to Nutanix and enquire about a hosted POC where you use a playground environment hosted by Nutanix. 

if you have valid nutanix contract, it will show you under downloads.
otherwise as ​@jarrodl mentioned you can use Nutanix community edition or ask a your Nutanix presenter to provide you AHV.
Please note that AHV itself will not work and you must have AOS available as well.

If I download the community version, can I install it on my server and test the system?

yes, that is the purpose of community edition.
Please refer to provided link https://next.nutanix.com/discussion-forum-14/download-community-edition-38417 and enjoy using it  :)

Yes, The community edition is a free version designed exactly for that. Getting an introduction and playing around with Nutanix.
 

Here are some resources that can help you get started since there are hardware considerations.

https://portal.nutanix.com/page/documents/details?targetId=Nutanix-Community-Edition-Getting-Started-v2_1:Nutanix-Community-Edition-Getting-Started-v2_1

Jeroen has done a lot of work with the CE and has some amazing resources:

https://www.jeroentielen.nl/ce/

If you have any questions along the way, may sure to ask in the community edition section of the forums

https://next.nutanix.com/discussion-forum-14