It might be helpful if you show us the relevant part of the relationship graph.
Some things that may get you started:
1. related fields just put on the layout will only show the first child record (by sort order in the relationship, or by creation order if not sorted)
So, yes, you can put many related fields on the layout. If they are all one-one, then you should have no problem even with different relationships.
2. Summaries can be tricky with related fields.
a. if the calculation is for Count(relatedTable::field) in the parent table, it will show only the count for the relationship.
b. if the summary field is in the child and placed in a portal, it will honor the relationship and even any filters on that portal. This is handy for filtered portals! Sometimes this is just a single row portal showing the summary field.
3. The summary field in the child records can be used in a standard list view sub-summary report (also showing related parent fields, if desired). It relies on the sort of that report.
4. The GetSummary() is another way to get a value without the sub-summary report in children. But it does use the summary field and sort fields to get the correct values.
If you have questions on any of these, let us know (along with those screen shots!)
The use of multiple fields for the same data Ticket 1 Ticket2... Pass1, Pass2 suggests you may other issues with your data model that complicate your report.