If you can find a cheap engine and reasonable mechanic I would budget minimum £1000 all in. Too many variables to give you an accurate figure. I would suggest shopping around and getting a proper diagnosis first.
Probably a blown turbo or possibly oil pump chain. Is your oil pressure warning light on? Without stating the obvious you really shouldn’t be starting the engine if you want to try and salvage it in some way..
I just noticed it’s an ictdi not an idtec. More likely a blocked inlet and also clogged egr and intake runner control. Are you in the UK? You may want to consider booking with me for a health check
It’s normally when your VSA modulator has lost its calibration. You’ll need a Honda HDS to carry out a neutralisation procedure. I can do this, I’ve done it from time to time
The fact you’re not getting any dtc codes with such a profound issue suggests you’ve got some error suppression going on in the remap. It may well be the egr but ideally you want it flashing back to stock and then running some diagnostics. Get in touch via PM I can probably help.