To answer your specific questions:
1- If i get a full battery and i go on HEV mode, does the PHEV battery goes down or it os not affected on the charge left. (HEV battery vs PHEV battery)
If you force the car into HEV mode when the battery is full, the charge level will be mostly unchanged while you drive in HEV, but it will likely change a little bit. It might drop by a couple miles, depending on lots of different variables. It's still using the battery for regular HEV drive, just to a much lesser extent than it would in EV mode. It also charges (through regenerative braking, etc.), so you may not actually lose much or any charge. It depends on how you drive, and other factors.
2- Can the HEV system recharge the PHEV battery ?
The HEV and PHEV battery is all one big battery, despite your dashboard meter making it look like it's 2 separate batteries. Yes, the car can charge the battery enough to add EV miles, but it usually won't charge the battery much after it achieves 25% charge (which is when your dashboard meter shows 100% HEV battery and 0% EV battery). For the reasons explained in the post above this one.
On very long, very steep downgrades, I have gained as much as 4-5 miles of EV battery range from the car recharging itself, but this is VERY rare. In 7,000 miles of driving my car, that's only happened one time. Usually, the meter will sit at "0 EV miles remaining" indefinitely until you plug it in. The car usually only tries to maintain about 25% battery charge to keep the hybrid system operational, it does not normally try to recharge itself much beyond that, because that isn't efficient, but on the rare occasion when the car is regenerating excessive amount of energy from downhill braking, it will indeed dump it into the PHEV battery. Just don't expect that to be a common occurrence.
Last edited by cockedandglocked; 12-17-2018 at 02:21 PM.