Alexsv_17

Hello Z fans,
First of all Happy New Year to all the members of the forum!
​​I am going to give you some background info before I ask the questions.
In late summer I bought my 350z (a 2003 model with an HR fitted under the hood) with aftermarket front calipers and almost no brake pads left (the inner ones were almost scraping on metal). Also I noticed that the engine oil level was slightly over the max level but I didn't bother then.
I changed the pads 3 months ago (no issues whatsoever after that).
This week I changed the oil and filters and filled in just above between the Min/max of the dipstick.
The day after the oil change, my brother was driving the car out of town, revving it up when both of the front brake calipers started seizing up gradually according to him. He had to drive 20 miles back home with stuck calipers. When he finally came home the rotors were very hot and the car was hardly moving.
Because I knew the calipers itself were in good condition I search for the problem elsewhere. There were no cracks on the brake hoses, no leaks from the master cylinder itself or between the master cylinder and the brake booster. I then checked the vacuum hose and the check valve from the engine to the brake booster. No cracks, all working perfectly.
Then I used this site as a guidance to check the brake booster (https://axleaddict.com/auto-repair/Bad-Brake-Booster-Check). All seems to be fine except the misfire point. When I depress the brake pedal at idling the engine starts misfiring (no engine codes though). Then when I clamped the vacuum hose between the check valve and the booster and depress the brake pedal - no issues whatsoever. According to the abovementioned site this means a faulty brake booster which needs to be replaced.
I am not a mechanic and I admit I didn't know that a faulty brake booster can influence the idle speed of the engine. Now that I know this, I am pretty sure that I bought the car with the faulty brake booster and it didn't develop afterwards (because it had the exact same issue with idling when I came to a stop at a traffic light for example). I reckon it is because the previous owner drove with almost no pads and put a lot of pressure on the system.
Now my questions are:
1. Is there a relation between the oil level and the amount of the vacuum the engine makes to the booster.
2. Could it be the pumps of the master cylinder at fault
3. If I try to restrict the amount of pressure the engine makes to the booster (by clamping the hose partially) can I drive the car without fear of that happening again before I change the booster.
4. How do I know which exact booster I have mounted (the car being a 2003 model with an HR fitted). Is there a part number stamped on the booster. From what I researched there are couple of part numbers there for the booster ( I think this one fits all the years 47210-CE400)
I am sorry for the long post, but last time I wrote you guys were very helpful and spot on, so I hope you give me your thoughts on the matter.
I forgot to mention that before I started testing the brake booster the front wheels were still stuck, and now they are fine. I didn't drive the car I checked by jacking the front end and spinning the wheels.
Thanks in advance to everyone,
Alex