Is there any way for me to pass information from the installation node to the program node? For example, if I wanted to save a specified value in the Installation node and then be able to access/have my program node vary based on that installation value, is there any way to accomplish this?
No - generally not between singular instances of program nodes in a program tree.
However you can from a parent node access and interface with child program nodes, if they provide you with a supported API. E.g. built-in nodes such as Waypoints or Set commands provide an API for you to configure them. If you need to do the same with your URCap-child nodes they need to implement a custom URCap API, as described in the “program_node_configuration” document section “URCap Program Node proprietary API”.