Good advice from ThePoetaster.
Both attempts were your fault unless someone else was driving...
The two faults you mention are indeed common serious/dangerous faults. Clearance of obstructions can be anything from a fault to a dangerous depending on the road, other traffic, speed and distance. If you are getting too close you’re not allowing for doors opening, wing mirrors, not to mention how uncomfortable it is for a passenger to be flinching when passing parked vehicles. You should be able to judge distances and guide the car without getting too close.
Following distance is self-explanatory. If the vehicle in front comes to a stop for any reason, do you want to be able to stop using your brakes or using your face against their back windscreen? There is no excuse to get this wrong. 2 second gap in the dry, 4 in the wet, 10 if icy. If you are getting too close, you are losing concentration - obviously a problem.
There are obvious reasons why driving tests aren’t decided on what the candidate ‘thinks’ is a fault.
There are also reasons why we have some of the safest roads in the world.
This is the cheapest phase of your motoring. How are you going to afford a car/insurance/servicing/fuel?
Take it seriously, well done on taking more lessons, and best of luck for your test.