Everyone has their own opinions. Induction gains vary from car to car even with the same engine, 12hp is not unusual if the original is a restriction. However, also easier to lose hp than gain with an induction kit. Manufacturers' claims are useless.
Cat restriction again depends on car. Clogged cats are always a problem, however standard cats often aren't a huge loss on non-turbo cars. I think it is always better to leave the cats in if you can. Can have unintended consequences with the exhaust note/booming.
FPR can give small a benefit to fuel economy, due to better atomisation, and support gains from cams, etc. Best if chip/remap is set for new FPR. Will throw off trip computer.
A big car like an Omega isn't going to see the same benefit from a lightened flywheel as a lighter car. It also degrades the comfort, especially if replacing dual-mass, which is what an Omega is more about anyway.
In short, the only sure route is to listen to people that have done things to the same car you have, and hopefully have RR results to prove it.
Yes all good, can't beat a good sounding exhaust note!
My drilled airbox sounds great too, nothing better than hammering up behind someone and booming past them on the open road

Sorry for my opinions as they're clearly off the 'norm' for this site, but I am 23, have owned tuned astra GSi's and GTE's before this, and have bought the omega as a fast family car (as I have a 2year old son), so when I'm in it on my own speed is of the upmost importance. Until I have 200bhp I won't be happy with it, as it's horrendously slow at the moment. Any gains I can get, however small are important to me.
It will also be visiting the 1/4 mile strip and track days in the future so acceleration is also very important to me.
LSD will be fitted soon too.
I'm not a 50+ year old who needs a comfortable and quiet cruiser.
And fuel consumption is not important to me at all.