Brakes, chainset and rear mech will be fine. I suppose it is possible (but I think unlikely) you’ll need a longer hose to the rear brake – probably depends on the routing on the respective frames.
You’ll have to check the clamp size on the front mech (you need 34.9). Your current one will probably have the size marked on the inside of the clamp. However a new front mech will be peanuts on eBay due to the current popularity of 1x gear systems. I’ve several spare front mechs, unlikely to ever be used (by me)
Is your current rear wheel and ‘old fashioned’ QR skewer – that’s what you need
I don’t know what the head-tube size of your On-One is but I’m pretty certain you’re going to need a new headset.
This from the Cotic site:
‘Our new frames have adopted the external bottom cup regardless of whether you’re using a 1 1/8″ steerer or taper. Whilst a regular zero stack bottom cup will fit if you’re using 1 1/8″ forks, it steepens all the angles by 0.5deg and more importantly for frame longevity, you will have no fork adjuster clearance to the down tube so using zero stack bottom cups has strong potential for damaged forks and frame as well as slightly shady handling. Hope have this completely covered with their new 2H headset. This has a crown race adaptor you can use for 1 1/8″ forks leaving you free to upgrade to taper in the future without changing your headset.’
Check out Cotic’s webby thing. There’s a wealth of info on it.