Before answering your questions, i have some comments about your design.
1- As we see in the picture you attached, each stack has 3 switches, one of them will connect by 2 links to the 2900 switches.
I suggest you connect the second link from the last switch in the stack, so 3 switches in the stack each two of them will have a link (at least) to one of the 2900 , and for better performance and redundancy 2 links will be better.
2- Again in the stack, i suggest you connect the first to the last, you have 3 switches, so connect 1-2 and 2-3 then 3-1 for better redundancy.
Now, configuration wise, if you have each stack in one Vlan, so just keep the stack without any configuration (an IP address in the same range of its Vlan for management) and create all the Vlans on the 2900, and untagg each port connect to a stack to an equivalent Vlan, then tagg all the Vlans on the uplinks from 2900 to the 5400.
Each stack's Gateway will be the IP address of the Vlan on the Routing Switch. Say you do Routing on the 2900, so the default gateway for Stack 1 will be Vlan10 IP address on the 2900.
And if you are doing routing on the 5400, then again the default gateway of the stack will be the Vlan IP address on the 5400.
Suggestion: Do routing on the 5400, so you can control traffic between Vlans by using ACLs, and i suggest the redundancy on the edge that i mentioned above.
Redundancy on the Core can be achieved by running VRRP, but you need the Premium License for both 5400.
Also you can run MSTP for a fast L2 redundancy and better performance, and you can do that by creating an MSTP domain where Core1 is a Root for 3 or 4 Vlans, and Core2 is the Root for the rest 3 or 4 Vlans.
The only reason i didn't comment about the 2900 is that you connect them to both core with 10Gig links, otherwise i prefer to replace the 2800s with 2900 that has better performance and you can link to core by 10Gig but in this case you will have 2 Layers, Edge and Core and i prefer that solution (from my point of view) .
Anyway i suggest you to keep your solution scalable and ready for future expansion, so the 2900 on the edge is better that 2800 because it has 10 Gig links and mush better switching capacity.
Based on the design you made, i prefer you connect all the stack switches together with resilient links and run MSTP on all the switches, and VRRP between the 2 Cores.
And i prefer you link the 2900 to the 5400 by 10Gig links, (anyway you can't achieve by using the 4 10Gig links more than 28.8Gig).
