Select column from ALL tables

I think what you're missing is a car_configuration table. This will have an FK to the cars table and have car_config_parts and car_config_tunings as children, like so:

create table car_configuration (
  config_id integer primary key,
  car_id integer references cars (car_id)
);

create table car_config_parts (
  config_id integer references car_configuration (config_id),
  part_id integer references parts (part_id),
  constraint car_config_part_pk primary key (config_id ,part_id)
);

create table car_config_tunings (
  config_id integer references car_configuration (config_id),
  tuning_id integer references tuning (tuning_id),
  constraint car_config_tuning_pk primary key (config_id, tuning_id)
);

You can then include the config_id as a reference in the timeset table (with no reference to cars). You'll need to ensure that you can't change the parts and tunings for a configuration or implement some form of versioning on this table to ensure you can reconstruct the exact details used to set a given time in the past.

I would go with the single-table option. It's simpler and I don't see any reason why you would need two tables in this case. If you want to make it easier to find records with status of "2" or "3", you could create a view that only displays these.

The only reason I could see for having two tables is if inserting/updating with a BLOB is very slow and causes performance hits for queries on the same table.