And because my German is even louser (mostly passive) than my English I hope you won't mind me answering you this way.
"Odložená dovolená" – yes, postponed vacation. Maybe it's that they wanted to visit this very place last year but in the end they went somewhere else; or maybe they wanted to leave a week ago but then there were some urgent matters at work.
Lebensgefährich sounds fine for me. Would it make more sense to you if there was "šlo o život" – so roughly something like "es ging um Leben oder Tod"? Because I think "bylo to o život" here is such a short version of "byla to taková situace, ve které šlo o život".
"Když podnikáme výlety" can't be used here. Perhaps you've mistaken "těšit se na něco"/"sich freuen auf etwas" with "radovat se z něčeho"/"sich freuen über etwas"? (Actually, you can also say "těšit se z něčeho" but I'd say it's not that frequent.) If it's the first meaning then the following clause has to be in future tense because you're looking forward to something yet to happen. So perhaps there should be rather "das"s than "wenn" in your translation? Plus "těšili jsme se" is in past tense!, they were looking forward to the bike trips – at that time they didn’t suppose any murderous heats would come.
Těšili jsme se na výlety. Těšili jsme se, jak/že budeme dělat výlety.
Měli jsme radost z výletů/Výlety jsme si moc užili. Měli jsme radost z toho, jak/že děláme výlety (this last sentence feels a bit forced to me however, I’d probably say it very differently).
There are constructions beginning with čím: "čím dál (tím) víc/větší", meaning "more and more" (Bylo mi čím dál víc zima. Byla mi čím dál větší zima.) and "čím-tím", meaning "the more-the more" (Čím víc je zima, tím hůř se mi dýchá.). "Mehr and mehr" is just how it should be, I’d say. "Má větší sledovanost" in Czech would be right but "má čím dál větší sledovanost" highlights the gradual growth and indicates it’s a trend. (Okay, "čím dál" doesn't need to be here because "rok od roku" does the same thing but it sounds natural to put it there.)
In case you ask mainly why it's in instrumental then my answer is simple: I've not the least idea.
It's used this way ... when I think about it now it would be more logical to say "o co víc" than "čím víc" but in the past the instrumental might have been used differently and it was more logical back then ... just a suggestion.
Sledovanost is a standard marketing term used in media branch. Hmm, rating?
..., kde mají malý krytý bazén s tobogánem, vířivkou, párou atd.
..., wo sie ein Hallenbad (überdachtes Schwimmbad) mit Rutschbahn, Whirlpool, Dampfbad usw. haben.
What is the problem here, word choice? It seems right to me but I can't confirm it is. Anyway, ein kleines
(Or is "Hallenbad" automatically small?