Itemizing services per student at multiple schools by provider

Part of my duties is to record the services done by providers for students at different schools. Each week, I am given the provider's time sheet where it records the different services done for those students.

What I need to do is to record those services in an itemized fashion, which is then combined into an invoice each month.

There should be one invoice per school site, upon which the following fields are all included: service, student, provider (which I have set up as a class), and rate. Essentially, it should look like this --

There are 2 things I want to figure out:

1) Linking students to schools, but still itemizing services on invoices
2) Creating an invoice based on individual services which were noted elsewhere

Point 1--

In the past, we've had trouble with invoicing where students were accidentally put on the wrong school, leading to delays and issues in payment. As such, I want to make sure each student is specifically linked to their school, and only shows up in connection to that school. I currently have them set up as sub-customers where the parent customer is their school site, but invoices must be created for each school site which itemizes the services provided per student. What I really need is to be able to create an invoice for the top-level customer (school), then choose from the list of students attached to that school, then specify the service provided for that student. If a student has 3 therapy sessions that month, ideally it should show each session separately, not grouped together.

Either the student should be in a drop-down which is only available for one school, or there should be a way to display all services provided for students grouped by school, then to turn that group report into an invoice for that school site.

Point 2--

Is it possible to record all services provided for one student, then create a report for the school site which combines all of the school's students which had services provided for them? That is, I want to create the first example without having to manually enter everything into that invoice.

I feel like what I'd need to do is create individual student-based sheets which look like this:

And the hope is that I could then turn those individual student sheets into the invoice shown at the top without having to manually re-enter the data. I'm just not totally sure sort of thing I would have to set up per student, because setting up an invoice and then making an invoice from a batch of other invoices doesn't seem quite right.

What I'm really trying to do is find a way to enter each service one time, then have it automatically linked in various reports to reduce potential error in invoicing.

If I have to manually enter data into the school's invoice, I want to know how to make sure only students associated with that school show up in the creation process.

If I have to manually enter data into something for a student, I want to make sure I can then create an invoice for the school based on that.

Either is fine with me as long as I can make one invoice for that school with this linked data.