Hi,
I have answered for few of your questions with my understanding. Please refer the link pasted at the end which will answer rest of your questions.
-Can a parent consult a child's routing table?
Always the child's routign table refers the parent's routing table for the route that doesn't exist in teh child' routign table. The default route domain is 0 (Default Route Domain). If you create a new RD, it has the sequence of 1, 2 and so on. So, the default route look-up starts from child routing table towards parents' and then parent's parent's.
-Is the point of the partition default RD really just avoiding using %N notation?
%N notation refers the route domain ID. For example, if we have two RDs i.e., RD1 and RD2 created for two applications, that is defined by vs%1 and vs%2. Here %1 and %2 refer the virtual servers that resides in RD1 and RD2 respectively.
--Does this require a parent/child relationship?
It is not necessary to have parent child relationship. If you don't explicitly define the relationship, it will lookup in parent domain for the routes. But it would be better to have the relationship for effective routing.
--Can this occur if the RDs are in different APs?
For administrative partitions other than Common, you can create a route domain and designate it as a partition default route domain. A partition can contain one partition default route domain only.
The benefit of having a partition default route domain is that when you create objects such as a virtual server and pool members within that partition, you do not need to specify the ID of that default route domain within the addresses for those objects. For example, if you create a partition default route domain with an ID of 2 in partition A, the system automatically assigns any partition A object IP addresses without a route domain ID to route domain 2.
If no partition default route domain exists within the partition, the system associates those addresses with route domain 0 in partition Common.
-Can a Pool contain Members in another RD in the same AP, I assume so?
-Why can a parent exist in another Administrative Partition (AP)? Common AP yes, but others?
-If Strict Isolation is disabled (enabled by default) on all RDs can all routing tables be used?
-Why does it appear that you can assign VLANs from the /Common AP to route domains that are not in the /Common AP?
-What are the rules around ingress and egress?
--Can client side traffic ingress through one RD and egress through another?
--If so, does Strict Isolation need to be disabled?
Please go through teh folowing link to understand and hope it will answer your query fully.
Reference Link:
https://support.f5.com/kb/en-us/products/big-ip_ltm/manuals/product/tmos-ip-routing-administration-11-3-0/2.html