Will HA work when ESXi4.1 or older version of ESXi is added to newer version of Vcenter?
Yes, but for ESX/ESXi 3.5 you need make sure they are updated to a patch level that supports High Availability: VMware KB: Unable to add ESX 3.5 host to High Availability cluster or remove ESXi 3.5 host from main...
As per me, It will work. but as with every release there is improvements in HA wherever required, tt is always recommended to keep both vCenter and ESXi host on the same version.
Also it is not recommended to add hosts with different version into same vSphere cluster.
Please refer below vSphere HA requirement across 5.0/5.1/5.5 (more or less same), if you complaint with these requirements, it will work :
vSphere 5.5 Documentation Center
HA best practices:https://www.vmware.com/pdf/vsphere4/r40_u1/vsp_40_u1_availability.pdf
.
how HA will work in this case, will it work using aam or fdm?
if aam then when Vcenter and how it will decide (i mean at which stage) to use a specific agent where its log will be saved?
also how will the protected and unprotected vm will be accounted at Vcenter level will there be any difference in that?
I will dig into it and will come back till tomorrow IST.
... will it work using aam or fdm?
Once the host is added to a HA cluster, vCenter will install its current binaries on the host, no matter which ESX/ESXi version you use.
André