Keeping the condition of a consonant?

I have restarted my Russian and find again a problem. Abt soft and hard vowels. I have a list of hard vowels: а, э, ы, о, у. It is said: "When a noun, adjective or verb ends in a vowel from this list, it means that the previous consonant is hard and to keep this 'hardness' a vowel of the list of hard vowels should be used along the declination / conjugation". OK. So стол, стола, столу, столом. But столе? Here the hard л becomes soft because оf this "e" and not "э". The examples given make it rather confusing . It is said "After hard consonants: C + e стол-е After soft consonants : Сь + е читатель+ е . Perhaps the better is to asume that the condition of hard consonants changes before "e" in these cases and full stop. What do you think about it? Thanks

When a noun, adjective or verb ends in a vowel from this list, it means that the previous consonant is hard and to keep this 'hardness' a vowel of the list of hard vowels should be used along the declination / conjugation

This quote has some discrepancies. It's grouping too many unrelated systems together. (Reading, writing, spelling, declension)
It's important to note, the vowels themselves are not considered hard or soft. Generally, following a consonant, which one of a vowel pair [а - я] is used indicates whether the preceding consonant is hard or soft.

>When a consonant is followed by one of the hard-indicating vowels, the consonant is hard, vice versa: soft-indicating vowel indicates that the previous consonant is soft.
> When a consonant is not followed by a vowel (end of a word, or with another consonant after it), then the hard and soft signs are used to mark its softness or hardness.
(These two core concepts come from a reading perspective)

When declining:
стол is pronounced with a hard л, and yes, indeed, столе uses a soft л on the end.
This is because the Prepositional ending -е only comes as it is, it doesn't have a -э counterpart, and it does in fact change the softness of the consonant after which it is added. I guess, in a way, it is an "exception" to the idea that consonants keep their softness. But for sure, this idea is NOT a rule.
конь -> коне
карандаш -> карандаше

Think of it like this:
The prepositional ending is -ye
Whereas other endings are just the vowel, for example, -a (masculine singular genitive); so when you add -a to конь "kony", you get "konya" - коня. And kony + ye is redundant so it becomes simply "konye"
Most endings aren't adding a y, but do try to preserve any y that is already there.

Other endings do come in "pairs" in order to still mark the consonants as what they normally are (because the endings, unlike e, don't change the consonant):
-ый -ий (nominative masculine singular adjective ending)
-ом -ем (Masculine Instrumental singular noun ending)
-ами -ями (Either gender noun plural instrumental)

Spelling Rules will also come into play here. I haven't learned any of them specifically, after a while breaking them just naturally looks wrong.
https://www.youtube.com/watch?v=Yp4VoIQ98pg

ш is always hard. No matter what. "хорошо" - "шёл" , same ш sound, followed by the same o sound. Both soft and hard indicating vowels sound the same after ш.
щ is always soft.
ч is always soft.
ж is always hard. жечь - жаль --- same ж sound

Also note that о has two soft indicating brethren - е(when unstressed) AND ё(when stressed).

Thank you for your complete answer. I will print it, read carefully and keep near the mentioned text. Again, огромное спасибо.

Dear xXHox,
I have just translated your answer in order to study it easier. Really your explanation is very clear and complete. If you are a teacher it is a luxury for your pupils having such a good teacher. Thanks again.