A watt of solar power is a watt of solar power.
No.
Solar panels are rated for capacity in "peak watts". That means: the solar panel will produce one watt under an illumination of 1 kW/m2. 1 kW per square meter is, roughly, the intensity at noon on a cloud free day.
If the illumination is not 1 kW/m2: it will not produce one watt.
It means nothing in regard to day time or cloudness.
If it is cloudy, a 1-kW solar panel will not produce 1 kW of electrical output. If it is after sunset, a 1-kW solar panel will not produce 1 kW. Time of day and cloudiness determine the power output.
E.g. no one prevents you to build your 1kw plant to point to 15 O'Clock and have the right angle to produce '100%' of its rated yield in September and April.
That is correct. You can chose which way to tilt your panel, which will set what time you produce peak power. It's not always best to tilt at the angle to maximize integrated power.
Noon is only relevant if you are so stupid to point your plant right now to due south at 12:00 in July. (And the energy difference of a proper angled plant for 15:00 in September or 12:00 in June is less than a percent)
For a tracking collector, that's probably about right. For a fixed-tilt collector, the loss is a bit more than that. The output goes as cosine of the angle, times the air mass factor (which to first order we can neglect). Since the sun moves 15 per hour, going from noon to 15:00 you lose by cosine of 45, 0.707 (about 30%).