Can I buy the standard off-peak return to Birmingham Intl, but leave and walk through the barriers at New Street?
Yes - as with most Off-Peak Return tickets, there is no restriction on breaking your journey on either leg of a Kettering-Birmingham ticket (whether that's Birmingham New Street or International). This is because the restriction code associated with the ticket is 2V, which as you can see at
www.nationalrail.co.uk/2V does not carry any restriction on break of journey in the same way for example 3A (
www.nationalrail.co.uk/3A) does. Going via New Street is an eminently reasonable, as well as permitted, route.
For future reference, it's easy to find out the restriction code of a ticket by going to
www.brfares.com and entering the details of the journey covered by the ticket. All the different types of through tickets available for that journey will be shown, including details of any restriction codes applying to each ticket. One word of warning - whilst prices and restriction codes etc. are updated daily, the text for restriction codes can sometimes be quite out of date (it's an issue they're working on fixing). Always check the text of the restriction code on
www.nationalrail.co.uk/XX to make sure you've got the up-to-date information.
As I need to leave New Street quite early (8amish) on the Monday morning am I correct in thinking I can't use the remainder of my "off peak" ticket to complete this journey?
Yes you can - on the outward portion of a (Super) Off-Peak Return, it is valid for travel up to 04:29am on the third day of validity. The only restriction on travelling beyond the first day of validity is that London Underground will not accept such tickets for cross-London transfers beyond the first day of validity. However obviously if you wished to resume your journey before 09:30 on a weekday then you would theoretically need to excess your ticket to an Anytime ticket - a rather expensive excess I'd imagine. It may be cheaper to get a new ticket for New Street to International - the tickets are not very dear.
It's unlikely that you would undergo a ticket check on-board in a journey that short (and in any case they usually wait until after Coventry or Rugby to check tickets on most services, at least on WMT or VT). It's more likely that you'd get (rightly in this case) issues at the barriers at New Street and/or International.
So all you need to complete your journey in theory is the one ticket, Kettering to Birmingham International Off-Peak Return. It may, however, be cheaper to obtain multiple tickets for this journey - and there are accredited websites which will sell you a combination of tickets for your journey in conjunction with a single itinerary, booking confirmation and pick-up code, such as
www.trainsplit.com.