What is the gravitational force between two masses of 15kg each, when their centers are 0.25m? could you detect this force with even sensitive equipment?

Well I don't know !
Let's work it out.

The gravitational force between two objects is

                     F  =  G  ·  M₁·M₂ / R²     .

'G'    is the 'universal gravitational constant'.  We could look it up. 
'M₁'  is the mass of one object
'M₂'  is the mass of the other object 
'R'    is the distance between their centers. 

It looks complicated, but stay with me.  We can do this !
We know all the numbers, so we can calculate the force.

'G'    is  6.67 x 10⁻¹¹ newton·meter² / kg²   (I looked it up.  You're welcome.)
'M₁'  is  15 kg
'M₂'  is  15 kg 
'R'    is  0.25 meter.

Now it's time to pluggum in.

       F  =  G  ·  M₁·M₂ / R²

           = (6.67 x 10⁻¹¹  newton·meter² / kg²) · (15 kg) · (15 kg)  /  (0.25 m²)

           = (6.67 x 10⁻¹¹  ·  15  ·  15 / 0.0625)  N·m²·kg·kg / kg²·m²

           =      2.4 x 10⁻⁷  Newton  .

That a force equivalent to about  0.00000086  of an ounce.
This is the answer to part-a.

Concerning the answer to part-b ...
Personally, I could not detect this force, no matter what kind of equipment
I had. But I am just a poor schlepper engineer, educated in the last Century,
living out my days on and getting my kicks from YouTube videos. 
I am not pushing the box to the envelope, or thinking outside the cutting
edge ... whatever.
I am sure there are people ... I can't name them, because they keep a
low profile, they stay under the radar, they don't attract a lot of media
attention, their work is not as newsworthy as the Kardashians, and plus,
they seldom call me or write to me ... but I know in my bones that there
are people who have measured the speed of light to NINE significant figures,
aimed a spacecraft accurately enough to take close-up pix of Pluto ten years
later, and detected gravity waves from massive blobs that merged 13 billion
years ago, and I tell you that YES !  THESE guys could detect and measure
a force of  0.86 micro-ounce if they felt like it !

50 meters per 5 seconds

Ireally don’t know