From your list the only real non independent "wa/وَ" is in
which is a plural form of the verb: وَجَدَ.
In all other posted cases "wa" is an equivalent to "and" and therefore should be considered as a different or independent word. I honestly don't know if there's really any rule saying one should "hang them" on the following word.
But how would you analyze the Quran linguistically if you don't even know which words can be separated and which not? You should first star by learning Arabic and try to know the roots of the words!
I mean if you take away those "wa" you would change the meaning in most cases dramatically, so that the sentences wouldn't make any sense. This would also have major impact on the grammatical rules -assuming there still will be some useful sentences left-.
IMO you should still elaborate your Question or try to explain how you would achieve what you want to do unfortunately I'm not able to follow your link as I'm behind a firewall!
As for why "wa" is so prevalent, one reason for that is the use of many "and's" in the Quran, also a lot of Arabic words start with "wa" as the verb already mentioned above an other frequent example in the Quran is
then it is used for oaths as described by goldenPseudo for example
وَالتِينِ وَالزَّيتُنِ وَطُورِ سِنِينَ وَهَذَا البَلَدِ الأمِينِ (at-tyn)
where 3 of the "wa's" are of this kind (the 2nd one in the order of the verse is an equivalent to "and")!
on the other hand as the letter "واو" in Arabic is one of the letters which appear especially at the beginning of a word like an independent letter. You may miss the fact that in Quran there are many words that start with a "فاء" / "fa ف" or "باء" / "ba ب" or other letters, which aren't a part of the "next" word like:
in surat a-Shams
and in some riwaya:
فلا يخاف instead of ولا يخاف
note that about all the rest of the verses of this surah begin with an oath.
or in surat al-qadr
in surat al-'alaq
just to give some examples from short surahs.
And Allah knows best!