Dimko, let me put it this way.
The root of the word Slav, i.e. in Slavic languages either as Sloven, Slovan, Slaven, Slavyan, Slovien, etc. is 'slov', 'slav' and then even further 'slo', 'sol'. It is the later form of the word Sun 'Sol' from which we get Solnce, Slnko, Slunce, etc. in various Slavic languages. From the root 'slov' we have 'sloboda' leter in Western Slavic 'svoboda' similarly is why the Slavic tribes in the West were called Suevi, Svevi, Suebi by the Romans; because Alveolar Lateral Approximant 'l' was switched in speeched by an Labiodental Approximant 'ʋ'. From the root 'slav' derives 'slava' glory, and from it the whole list of words you mentioned (but those
only derived later from 'slava' glory). The word Pravoslaven is a direct translation from older original Greek ὀρθοδόξια ('ὀρθός' right, correct - prav, pravo, pravda; 'δόξα' glorification, celebration - slava, slaviti). However, ὀρθοδόξια is today translated as 'pravoverie' - 'right faith'. Unfortunately, your attempt to explain Slavs as Orthodox fails short of reality. The word Slavs (Sklaveni in Latin) appears before they were Christianized and in territory where there the Orthodox Christians were never even a majority. The word Sloveni, Slovania, Slaveni, Slavyani, Slovieni in its original form represent a different religion and word and literally mean "Sun Worshipers" (not Pravoslav-Orthodox, which by its doctrine makes it's followers "Death Worshipers", just like the rest of Christianity with a belief in the 'Jealous male god of the desert').
It can also how other meanings like 'farmers' - selovani, and even a noble/ruling class meaning. In the early Middle Ages it meant ethnicity (Slověni) as well as language (Slověnski). Today it stands for the name of a group of peoples speaking related Indo-European languages.
The root 'slov' 'slav' derive from the older 'sol', 'sul' as I mentioned before, however, it derives from even an older version.
In many languages Alveolar Lateral Approximant 'l' is in fact derived from an older form: Alveolar Approximant 'ɹ' (
check this table for explanation). We mostly write 'ɹ' as just 'r' but it is an individual thing of how we pronounce it.
The older for of 'sol', 'sul' is 'sur', 'sru'. The first root being 'sar' which means high, esteemed, light, white, glorious. From this root we later have a myriad of words and meanings and an even greater myriad of different peoples and groups who had their name formed from 'sar' one way or another. The root 'sar' first forms the word 'Sur', 'Surya' which is the oldest name for the Sun in IE (Indo-European). Based on it, any group of people who have this root in their group's name are in fact "Sun Worshipers", and not only in theory as there are evidence for all of them that they in fact were "Sun Worshipers", "The Sun People": Suri. From Suri we later have Survi, Surevi, Surians, Syrians, Sarmati (Sarbati: Bilabial Plosive Voiced 'b' being replaced by Bilabial Nasal 'm' and sometimes Unvoiced 'p'), Surbi, Sirbi, Serbi, etc. Reflexion of 'rb' occurs as well, so we have Subri, Sibri, Sabiri. Alveolar Fricative 's' is sometimes replaced by Postalveolar Fricative 'ʃ' ('sh', 'š') so we have Šuri, Šurbi, Šumeri (Šuberi: Sumerians).
Another change occurred which is even more common, but more distant in terms of voices. While 'l' and 'r' are both Alveolar and 's' and 'š' are Fricatives, the next change that happened was between these Fricatives and the Velar, Uvular, Pharyngeal and Glottal i.e. the "back" vowels. These are shown in the
table I posted. The first example of this change is show in the two most oldest IE languages, Sanskrit and Avestan. An example (observe):
surəm damohu scvistəm
suram dhama
su savistham
miθrəm yazai zaoθrabyo
mitram yajai
hotrabhyah
(bold is Sanskrit, regular is Avestan)
I do not know the exact word for this change (from Fricatives/Sibilants to "back" vowels), but I do know the reversed proves which appears in Serbian and Slovak (because I learned it) and is called Sibilarization, for example 'noga' > 'nozi, 'ruka' > 'ruci', 'orah' > 'orasima', 'duh' > 'duševni', 'bog' > 'bože', 'ruka' > ručni' etc. However, in Slavic languages Palatalization is far more common and one of the main features of Slavic languages (changes from "back" vowels to Palatals).
There is also the phenomenon called Bethatism which occurs among the Labial consonants (Bilabial and Labiodental) mainly between Plosives (p,b) and Fricatives (ɸˌf,β,v). Such is the reason why Babylon is Vavilon in Serbian, or Byzantium is Vizantium.
The last change I would like to mention is when an Unvoiced consonant replaces a Voiced one and vice-versa: s-z, t-d, p-b, š-ž, etc.
The
vowels change among themselves much more freely and follow less rules than consonants. If you know how vowels are articulated you'll understand how they can change into virtually any other vowel.
Just to note. These changes do not just happen. It is a lengthy process of decades and centuries of conversation between peoples, the lack of certain sounds in some languages while abundance in other and replacing them when a foreign word is encountered (like why Greeks call Serbia 'Servia' because they don't have 'b').
So we have for example word 'zora' which means dawn, we have a lot of synonyms for the Sun, from both roots 'sr' and 'sl' like:
Sol, Kolo, Galo, Helo, Cyrcle (sur-sol),
Horo, Oro, Hero, etc.
Traditional Slavic dances all have Kolo or Oro, Horo, because it is the dance of the "Sun Worshipers", the ancient religion of all Indo-Europeans and wider. Nothing to do with Orthodoxy or Christianity which come millenniums later.
If you understood what I mentioned above then you can figure out for yourself how did the names of the following groups of peoples came to be and how they are all tied to the root Sur=Sun:
Serbi, Sarmati, Kimeri, Kimbri, Huritti, Asuri, Horvati, Sloveni, Kelti, Gali, Skoloti (Sokoloti),
Germani (Serbani

),
Helleni, etc.
To add to that, there are names of rivers (Srbica, Sirbis, Slovenka, etc.), mountains, lands (Siberia, Serbia, Slavonia, Galatia, Carpathia, etc.) that also have the same root connected with the Sun.
So there you have it. The root for Sun is originally present in nearly all Indo-European language groups and names of peoples. There are also a lot of roots that have a synonymous meaning like 'luk' and 'kiś', but about these another time. There is far too much of it for this forum and its members to handle and I only have a humble knowledge of it.
So to conclude, the root 'slav' is only a small part of the greater group of roots (conveniently most of them are gathered in the Dhatupatha of Panini). It can stand for
people, religion, culture, social class, a wide range of geographical terms and much much more.
And next time Dimko, think before you say anything. You act as an overexcited cheerleader, a phase which I regret going through myself.
What I wrote above took me two hours, but it is only a small part of the whole picture.