Lots of questions in there. First on the network. I'm not familiar with the Dell Power Connect switches but what you will need to know is if the switches support the equivalent of cross stack etherchannel. That is, can you take a port for each switch and bind then into a LACP pair. My guess in not. Thats fine though, it just means the you follow the other diagram in the TR that outlines when you don't have stackable switches. The configuration involves assigning 2 IP addresses in 2 subnets to the VIF on the NetApp and 2 vKernel IP addresses on the ESX servers. Then when you connect the datastores alternate between the IP addresses. Or better yet, use the VSC which will do this for you by default when you provision datastores.
Next for your backups. If you have 2 NetApp controllers I would highly recommend you leverage SnapVault to move the backups. If you leverage NFS on your new 2240, you can then set up a SnapVault target on the S250. Then take the backups with VSC which will be instant if you disable the VMware snapshots and fast if you don't, then SnapVault those backups to the S250. That vault can be mounted to your VMware environment as a read only datastores for simply copy and paste restores if needed.
The Vaulting today still has to happen as a post backup script with VSC using the SV-SMVI tool here on the communities (just do a search for it). You will find the SnapVault moves far less data and is much quicker than the Veeam option.
I don't know if the 250 is still supported though so that might be the only wrinkle in your plan regardless of the product used...