Yes, we do. You're correct that in British English have got is what's used, but at least in American English, we do say have gotten.
I've gotten 10 parking tickets already this year!
I have gotten almost no sleep since my baby was born.
In American English we use have gotten both when writing and when speaking. As Peter Shor notes, it sounds very odd to us to hear Brits say (or write) have got!
You might also be interested in this question on EL&U which asks about the difference between the two constructions and has some interesting answers.
The word former refers to state. It means that the person or object was something, but no longer is. The word "former" only refers to sequence in special cases where it is contrasted with the word "latter" (in which it means the first of two given items).
The word previous refers to sequence. It means that the person or object was/did something before something else took over or replaced it. As StoneyB rightly clarifies in his comment, "the previous" means the directly preceding member in a series, however "a previous" can refer to any earlier member in the series.
The word last, in this context, means the same as "previous", but is only used to refer to the immediately preceding item. (Jay warns that "last" can be ambiguous as it is also used to refer to the final entry in a series.)
Thus, you can say "former coworker" of someone who is no longer a coworker. However, the word "previous" means the one before the current, so saying "previous coworker" or "last coworker" does not make sense unless you had a coworker and they were replaced.
Referring to TV series, you can say that you preferred the "previous" or "last" show, and this would refer to the show immediately preceding the current show. You cannot say the "former" show in this context.
When referring to a show that aired earlier than the immediate previous, you can say "a previous show". Otherwise, you can be more specific. Depending on the circumstances, you might say "the first show", or "one of the earlier shows", or "episode ten", or simply "one of the older shows". You could even say something like "five episodes earlier".
Best Answer
Both are okay, but they might or might not mean something different depending on how you look at it.
Generally, "Whenever X, Y" means that X happened/happens/is supposed to happen many times, and each and every time Y also happens (or in this case, you're told to make it happen). So your sentence would read as a general rule - "you'll have many chances to hold onto happiness in your life, and each time that happens, make sure to do so".
"When X, Y" can mean a single occurence - X happened/will happen, and Y happened/will happen at the same time. So you'd rather say "...when you get the chance" if there's a particular chance to be had - for example, you know your friend is getting a new job, and he's being anxious for it, so you're telling him to hold onto that once he gets the chance (and that job). Compare "When you get that job, you'll be out of trouble" vs (technically grammatical, but making no sense). !"Whenever you get that job, you'll be out of trouble"
Now, what @Man_From_India said also holds - if the context or grammar already estabilishes that you're talking about a repeating occurence, you can use "when" in place of "whenever". For example, "Check your locks when you leave your house" can be placed in a health and safety guide, and it would mean the same as "...whenever you leave...".