TUHS3F05 without other components
I've checked the instruction manuals of the part. The parts that are used in the reference schematics are:

F1 :: Input fuse 

To prevent the situation when the power supply starts to draw much current, most probably because of some failures.

Eliminating this may cause damage to your parts and maybe power lines.

C1 :: Input Capacitor

To comply with conducted noise on the input and to reduce high-frequency electronic noise that may cause interference with the part.

Eliminating this may cause lots of problems in noisy lines or EMI prone environments.

Cbc :: Smoothing Capacitor

To smooth the output voltage and counter fluctuations that cause instability.

Eliminating this may cause instability on the output voltage.

R1 :: Inrush current protection resistor

To limit inrush current to avoid gradual damage to the component and avoid blowing fuses or tripping circuit breakers. 

Eliminating this, well, has a risk of damage to component or blowing fuses.

SK1 :: Surge Protective Device

To protect against transient surge conditions.

Eliminating this may cause problems for the component.

So to answer your first question: Yes, eliminating those parts can cause lots of short or long term problems and drastically shorten the life of the component.

If you have to go on with your schematics, keep that in mind that, you might saw lots of instability problems, but then again it all depends on the environment.

So as advice that I've learned the hard way, always stick to the datasheet.

And if you want to check other board mount power supplies, you may check the suppliers and like digikey.