Regarding the question raised in the title,
Is it possible build a telescope on a field of mirrors?
The answer to this question is a resounding "yes". A number of existing and planned telescopes use arrays of mirrors, depicted below. Noteworthy amongst them include the James Webb Space Telescope, which will use an array of eighteen hexagonal mirrors, and the Thirty Meter Telescope and European Extremely Large Telescope, both of which are absolutely colossal in size.
With regard to the second question,
Is it possible build a telescope on a "field of mirrors" like the image below?
The JWST, TMT, and EELT have one other colossal aspect to them: Their costs. I couldn't even imagine what the costs would be with regard to a telescope of that size.
With regard to the third question,
I mean, an energy plant on day time and a telescope in the night.
Absolutely not. The heat stresses that would inevitably result from daytime and nighttime use would quickly make the field of mirrors useless at night. There's no problem with using a wavy mirror to reflect sunlight towards the collector of a solar power plant. The quality requirements on the mirrors aren't very high. There's a huge problem with using a mirror that is even slightly wavy to reflect starlight towards the central optics of a telescope. The mirror segments in the arrays of mirrors used for those large telescopes need to be nearly perfect. Sunlight never touches them.