Travelling from Manchester to Belfast Int.

Why would a budget airline be any faster?

You still have to go through security, etc.

well I assumed that travelling domestically will incur fewer security checks ie be faster.

Nope and given the "terrorist" incidents in both cities over the years security checks are taken very seriously.

Terrorist incidents involving airports ?

Security at Belfast Intl has had a few high-profile delays recently due to lower capacity. You may need to be there well in advance of your flight.

Terrorist incidents involving airports ?

Not typically but recent letterbombs sent to Heathrow airport and other places have had responsibility claimed by people purporting to be from the IRA therefore expect security to be extremely tight.

1) You are "travelling overseas", over the Irish sea.
2) It depends on the airline.

Different airlines have different minimum times, both minimum check-in time and minimum time to be at the gate. Budget airlines generally require more time than do "full service" airlines, and they are stricter at enforcing it.
Easyjet requires you to be at the gate 40 minutes before scheduled departure. They have online check-in, however if you are dropping off bags, this will close some time earlier.

I suggest you check your airline's website.

well I assumed that travelling domestically will incur fewer security checks ie be faster.

Not true, security is the same for all fights. What you will be saving is immigration (passport control) when landing at Belfast. You will still need to show your passport (or possibly other ID) at the gate so they can check you are the person on the ticket.
"other ID" - what other ID they accept is up to the airline. The only thing you can guarantee 100% they will accept is a passport.

Thank you for all the help! The replies will certainly help improve the accuracy of my travel times.