IMO you should start with upgraded BRAKES! 
He spoke about swapping the na 1.8 for a turbo 1.5.I wouldn't even dream of adding even a low pressure turbo or supercharger to the 1.8L HRV
If you fit the transmission that is installed with the 1.5 turbo, that should negate this concern.I would be worried about the transmission holding the additional torque
What do you mean by engine management sorry?Anything is possible but if you are asking on this forum. Then most likely nothing off the shelf is available and unless you have your own shop. Buying parts is simple but installation and making it function will costs you several thousands for tuning and fine tuning. So it’s a no go, engine management is expensive and not readily available for under $3k.
Mines not a CVT as it’s Manual right? So I wouldn’t need to bother with that. Idk but I wanna know where I can find stuff for the car or universal stuff that fit on the car.If you have the CVT, you will need a stronger clutch, and possibly a new trans that isn't a CVT. Add that to the costs of programming that pearlwhite01 mentions, and you might as well just buy another car that comes with a turbo.
Good to hear, I got a quote from the guy and he told me €1000 for the full custom exhaust, which he will customise it for two exits, which is hard for the HRV cause it doesn’t have the grooves but he could do it, also with the price for the day that I will have to pass the vehicle road worthy test he will change it back to the original for free and so on, what do you think, only guy I could find to do it for meExhaust will add sound and better response and minimal horsepower. It definitely is a good modification. I have had several cars with exhaust systems. It’s something I will gladly spend money on.
Sounds like you need to do a TON of research before starting a project like this...What do you mean by engine management sorry?
where could I buy the parts though, I don’t know what to buy and where! Then I will deal with the rest
Hey buddy! I’m born and raised in Gibraltar@LenzoGIB Have a search online for Japanese tuning specialists near you, there is quite a market and set up for this in the UK, so may be the same where you are? The 2003 EP3 Civic Type R came with a na 2.0 and was able to be modified to the nth degree.
As for swapping the exhaust, not sure how sustainable financially it will be for the garage to keep changing the exhaust over for the ITV, considering they will have to do it twice for each ITV - off and back on. And the same for every year after that. You would also have to find storage for the unused one, and consider how you are going to carry the extra exhaust to and from the garage. There is also the insurance situation as well.
The European market had a MkII HR-V Sport 1.5 turbo that came with a twin exhaust, however, to accommodate it, Honda reduced the size of the underfloor boot storage to fit it in.
View attachment 35409
These were rare in the UK and only sold from 2019 - 2021, so the twin exhaust stands out, which may lead to you being pulled over if the Guardia Civil Trafico use ANPR like their counterparts in the UK do, and wonder why your non turbo HR-V spec vehicle has twin exhausts?
As an aside, Spanish flag with GIB in User name?