I would like to know if it is permitted to use a digital version of the Holy Quran for recitation, reading and such-alike, as the one shown in the video below:
Yes, it's allowed, as long as you trust that there's no distortion.
Allah says in Surat 'Āli `Imrān:191:
الَّذِينَ يَذْكُرُونَ اللَّهَ قِيَامًا وَقُعُودًا وَعَلَىٰ جُنُوبِهِمْ وَيَتَفَكَّرُونَ فِي خَلْقِ السَّمَاوَاتِ وَالْأَرْضِ رَبَّنَا مَا خَلَقْتَ هَٰذَا بَاطِلًا سُبْحَانَكَ فَقِنَا عَذَابَ النَّارِ
Who remember Allah while standing or sitting or [lying] on their sides and give thought to the creation of the heavens and the earth, [saying], "Our Lord, You did not create this aimlessly; exalted are You [above such a thing]; then protect us from the punishment of the Fire.
This ayah talks about "those who understand" in the ayah preceding it. The idiomic meaning of the expression "قياماً وقعوداً وعلى جنوبهم" is in any case and way.
There's a very essential rule in Fiqh that says:
الأصل في الأشياء الإباحة
The default state of things is permit
That basically means that a new thing is allowed unless it's contradictory to an existing rule.
Quran originally wasn't revealed in any physical form (unlike, for example, the panels of Musa -pbuh-), it was revealed gradually and the prophet and Sahabah memorized it, then later in the Time of Rashidi Khalifates, it was paper-written because many of the Sahabah who memorize it died, and so original "memorizers" are getting fewer.
Then, when printing became easy, prints of Quran entered every house to enable normal people to read and understand Quran, since the majority doesn't memorize it.
Any way that is intended to help people read Quran and understand it is very welcome, and the effort is thankful, Mufassireen tried to make Quran clear, their efforts are thankful, printers tried to make Quran books (mushaf) available, their efforts are thankful. And now comes technology time, and efforst are always welcome.
It's very welcome to try to digitize Quran so people can read it easily in, say, the Bus, the Metro... etc. It's very welcome to digitize it so search and research becomes easy (and we're being benefit from that here).
Allah says in Surat Al-Ĥaj:32:
ذَٰلِكَ وَمَن يُعَظِّمْ شَعَائِرَ اللَّهِ فَإِنَّهَا مِن تَقْوَى الْقُلُوبِ
That [is so]. And whoever honors the symbols of Allah - indeed, it is from the piety of hearts.
Trying to make Quran easy-to-read can be included in such meaning.
Is deleting a "Quran.pdf" destroying a copy of the Quran?
In addition to Ansari's comment, I would like to say that if you do that with a bad intention then you're sinful, else you're not so long as you do that in a respectful way. Muslims do destroy copies of Mushaf and there's no problem in that so long as they do that in a respectful way, there are preferred ways to do that, of course.
Yes it is right I also work with an Online Quran teaching academy most of our scholars use it, it's just matter of paper, you see in old times ppl used to use leaf, bones and woods to save some writings there was no paper in old times, similarly this is just a new shape of saving writings. just like paper.