I will correct your passage step by step. So, please keep patience

BTW, what is СЛР? I have no idea...

"Я работаю на пляже в первой помощи станции." -> Я работаю на пляже на станции первой помощи.

1) Sometimes it can be very difficult to provide some general explanation when we use "в" and when we use "на". The same is in English: I also make mistakes with English "in" and "on" sometimes. We say: "на заводе", "на фабрике" (in the factory) but "в больнице" (in the hospital), "в библиотеке" (in the library), but "на выставке" (in the exhibition), "на рынке" (in the market) but "в магазине" (in the shop) etc.
Maybe, it is a matter of history: when something is thought as a closed space (like a room or a building), we use "в" (therefore, в больнице, в библиотеке, в магазине). If something is thought as an open area, we use "на" (as на заводе, на фабрике - a factory is not just a building, historically it can be an area with many buildings; на рынке - again, market historically is an open area). The same comes with "станция": I think originally it meant mostly "a railway station", which is more an open area rather than a closed room. Currently, "станция" can have multiple meanings (same as in English), but we've got used to saying "на станции". Unfortunately, there is no other advice than to memorize it.

2) "something A of something B" is rendered in Russian as "noun A + noun B in Genitive": "station of first aid" is "станция первой помощи". I think it is similar in Hebrew.
English has also another possible structure: "first aid station", where noun B defines noun A. This structure does not exist in Russian.
Compare: there are two options in English: "government politics" and "politics of government", but there is only one option in Russian: "политика правительства", "правительство" being in Genitive.
Actually, you can also use an adjective and put it before the noun: "правительственная политика" (lit., "governmental politics"). But there are some limitations: 1) not all the nouns can form an adjective, 2) word combinations (like "первая помощь") cannot form an adjective.

"Но я не спасателя на водах, я фельдшер." -> Но я не спасатель на воде, я фельдшер.

1) Why did you write "спасателя"? To form the feminine? The nouns for people's occupation in Russian usually do not have a feminine version, the masculine form is used for both men and women. If you want to form the feminine, it would be "спасательница" (with adding a feminine occupation suffix, not just by replacing -ь with -я). However, "спасательница" would sound too colloquial, and is never used in more or less official speech.
But I think, you can say about yourself "спасательница" among your friends, if you like it.

2) "вода" does have plural: "воды", so "на воде" is singular and "на водах" is plural. But in Russian, the plural form "воды" sounds too poetic. In normal speech it is only used when talking about "waters" of some specific ocean or sea (e.g., "в водах Тихого окена" = "in the waters of Pacific"). Otherwise, use singular. So, your occupation is just "спасатель на воде".

"Я помогаю в случаях синяков, порезов, вывихов, вывихнул лодыжки, и также более серьезных случаев (или чрезвычайных ситуаций) как в случаях травмы спины, черепны-мозговых травм, затрудненного дыхания, сердечного приступа, остановки сердца, и так далее и так прочее." -> Я помогаю в случаях синяков, порезов, вывихов, в том числе, вывиха лодыжки, а также в более серьезных случаях (или в чрезвычайных ситуациях) как в случаях травмы спины, черепно-мозговых травм, затруднённого дыхания, сердечного приступа, остановки сердца, и так далее, и тому подобное.

Nice! Well done! I understand everything! Just a few mistakes:

1) You started with "Я помогаю в случаях ...", and then you list in what cases you help, using nouns in Genitive. Correct! However, than you suddenly insert a verb into the list: "в случаях синяков, порезов, вывихов, вывихнул лодыжки..." (past tense form). You cannot use a verb in this list, you need a noun. But the problem is you get a duplication: "в случаях синяков, порезов, вывихов, вывиха лодыжки...". That does not sound good. To avoid the duplication, I have rephrased your list as "в случаях синяков, порезов, вывихов, в том числе, вывиха лодыжки" ("в том числе" = "among others", "including", lit.: "in that number").

2) You started correctly: "Я помогаю в случаях ..." (в + prepositional). But then you forgot about it: "и также более серьезных случаев (или чрезвычайных ситуаций)". You have to keep using "в + prepositional" further on: "а также в более серьезных случаях (или в чрезвычайных ситуациях)".

3) We say "а также" = "and also", when you add another member to a list.

4) "и так прочее" - there is no such an expression in Russian. There are two expressions: "и так далее" (etc), "и тому подобное" (and so on). You can combine them if you like: "и так далее, и тому подобное", but usually either one of them is enough.

5) "черепно-мозговых" - "о" is the vowel commonly used to combine 2 roots into a single word (you wrote "ы").

6) "затруднённого" - that's not a mistake, we do write "е" instead of "ё". I just emphasized "ё" to make sure you pronounce it correcly. If you know it's "ё" and you write "е", it's OK.

"Мне нужно было часто делать СЛР в прошлом." -> В прошлом мне часто приходилось делать СЛР. or better: Раньше мне часто приходилось делать СЛР.

1) BTW, I do not know what is СЛР, and I am not sure Russian people understand it. Could you clarify?

2) Grammatically your sentence is correct. But your choice (мне нужно было) means "I needed to do something", like there was some necessity for you to do it. It does not suit logically. What you want to say is about your experience, not about the necessity, right? The expression "мне приходилось + infinitive" is exactly what you need.

3) Again, you use the time modifier (в прошлом) in the end of the sentence . Put it in the beginning, and you would sound much more Russian! And I would replace "в прошлом" with "раньше". Your option sounds as if that was long time ago in the past... and you have not been doing it since then. "Раньше" is much more colloquial and frequently used.