If I get a long distance off peak train (including a change) that leaves first destination at 10.30 and Cross Country at 1pm and arrives at 5, will that not be off peak because the arrival time is peak hours? Or does it go by the time you get on the train?
There is no such thing as an "off peak train" or "peak hours", you are misunderstanding the system, but you are not alone in this.
As
crablab has already said, when you have a ticket it will be endorsed with a restriction code such as "8A". What this code means you can look up at
https://www.nationalrail.co.uk/ticket-types/validity/8A/ and it's this which determines the restrictions placed on use of that particular ticket.
It's the ticket which determines the restrictions - if any - not the train or "peak hours".
You can look up fares and their associated restrictions at
http://www.brfares.com
If you have a specific question related to a specific journey you are planning, if you post your question here we will do our best to clarify for you.