Are these words common?

Hey guys!
I have some words that I want to know if they were common or not. (As usual it's in romaji sorry).
The words:
Seppatsumaru: To be at one's wits end, to be cornered, to be packed to the hilt.
Uchiakerareru: To be frank, to speak one's mind, to open one's heart.
Sonzai: Existence, being.
Chanto: Properly, steadily, seriously.
Hekomu: to feel down, to be overwhelmed, to be dented.
Bareru: to leak out (a secret{ to be exposed (a lie).
Massaki: the head, the foremost beginning.
Sukuu: rescue, save.
Omoikkiri: with all one's strength, with all one's heart.
Inoru: to pray, to wish.

(I'll admit it now, those words are from a song)
I'm sorry, I know that it might be annoying to read all of that and say if they were commonly used or not, but if you were someone who likes doing that please help. I appreciate your answers.
Thank you so much in advance!

Yes, they are fairly commonly used. Some are a bit casual (meaning I would use it only with my friends, not with colleagues, for example), but they are used.

Just some notes on it:

"uchiakerareru" comes from "uchiakeru/uchiakemasu," a verb with the meanings you've mentioned, "to confide (a secret)."
So "uchiakerareru" means "can confide in," like "kanojo wa nandemo uchiakerareru tomodachi da" (she is a friend I can confide in everything/I can be frank with everything). Also it may be "to be confided in" the passive form.

"chanto": the polite speech equivalent for this adverb would be "kichinto."

"hekomu/hekomimasu": a casual word.

"massaki" is most often used as an adverb, "massaki ni." As in "nyuusu ga kitara, anata ni massaki ni shirasemasu." (When I get the news, I will let you know first.)

All words you have shown are common in the sense of being used in everyday Japanese.

But their level of speech are different.
I have sorted them according to their difference.

1. Bookish and literary, but used in everyday life according to speakers' level of education:
Sonzai: Existence, being.

2. Common words, used commonly:
Seppatsumaru: To be at one's wits end, to be cornered, to be packed to the hilt.
Uchiakerareru: To be frank, to speak one's mind, to open one's heart.
[Uchakeru is the correct verb form (transitive verb form) which corresponds to your English. Uchiakerareru is its passive form.)
Inoru: to pray, to wish.
Massaki: the head, the foremost beginning.
[Ordinarily, this is used in the form of massakini, meaning "at the very beginning, first of all, at the head of" or in a locution like massakini susumu, meaning "to lead the way, to take the lead".
Sukuu: rescue, save.

3. Colloquial, but used very often in everyday conversation:
Chanto: Properly, steadily, seriously.
Omoikkiri: with all one's strength, with all one's heart.

4. Not necessarily slang, but very colloquial:
Hekomu: to feel down, to be overwhelmed, to be dented.
Bareru: to leak out (a secret{ to be exposed (a lie).

Thank you so much for answering so fast!
Then... Is it ok, if I learned words from a song like that but know which of them is a slang and which is fine to use(! (passive ECT ECT)

Then... Is it ok, if I learned words from a song like that but know which of them is a slang and which is fine to use(! (passive ECT ECT)

Yes, I think so. You can learn much from song lyrics.
I, myself, when I was young, learned more than a few words from Enlish and American songs. The important thing would be that you always check up on the usage of these words, because song lyrics, as far as they are song lyrics, could be somewhat poetic, or intentionally vulgar and exagerated, therefore not always suitable to everyday life conversation and normal writings (mail included).
Anyway, perseverance is essential in language learning.

Just to add, "omoikkiri" is a colloquial and emphasized version of the more ordinary "omoikiri". You can emphasize a lot of things using the same style such as "sugoku" vs "suggoku".

Thank you guys! you are always there to answer everyone's questions!