Been lurking on here a while so finally see something I can help with.
To answer some of the questions.
I wouldn't advise cycling on the Westlink, it is basically a motorway.
Getting out of Belfast wouldn't be a great start to a trip, I'm not 100% with Belfast but a route out would probably be something up past the zoo and heading the old road to Ballymena or something like that. If you get into Larne you'd be pretty much on the coast road straight away. Northern Ireland tourist office would give any help they could if you contacted them, possibly even e-mailing a shop like Slane Cycles or Dave Kane Cycles would give a good route as well.
The coast road is totally flat until you reach Cushendun, after that you've a 15min climb or so then it's downhill into Ballycastle. The coast road from Ballycastle to Portrush is hilly but worth it, the inland route is flatter but hasn't the views, when I say hilly I mean short and sharp climbs 100m>200m long.
On a good summers day you could do Belfast to the Causeway without to much bother I think, turn your two day trip into three and I think you'd enjoy it more though. Plenty of good campsites along the way, Cushendun/Ballycastle etc.
I'll be honest and say that I never found the Causeway super impresive, what you do want to check out are things like the Carrick-a-Reed Ropebridge, Whitepark Bay (just don't just stand at the top - actually go and walk it), Kinbane Castle (super scary walk down), Glenariffe Park (even just ride up through it to get the downhill into Cushendall), Bushmills Distillery (for the smells alone) - they are all along the coast route.
Portrush is the Blackpool of the north coast so don't expect much except arcades and chip shops, go further on to Benone and Downhill for more good beaches. The only downside I see is this, on the weekends the coast road turns into a race track for motorbikes, they ride in big groups and will ride close to you so it's something to be aware of. The roads themselves all have a good surface and people will stop if they see you're having a problem.
If you do come during marching season, you'll see a bit of drinking etc but on the whole if you get to see a parade I'd enjoy it for what it is, you'll not forget quickly the sound of a lambeg drum if you get close to one. Riding through Cushendall etc you've a good chance of seeing a game of hurling so I'd take 5 mins to go and look. Big events would be The Northwest 200 (motor bike race in Portrush), Lamas Fair (Ballycastle) and The Airshow (Portrush again)
Hope that helps!