Learn English – “I’m proud that you are the father”

Re "How can i find out if a turn of phrase is pleasant/good/valid?", writers.stackexchange will serve if you phrase your questions properly. Per its faq, one may ask about "Non-fiction, technical, or scholarly writing" and "Copywriting", among other genres, so long as you are not asking about "strictly interpreted correctness of English grammar or syntax rules".

In the first collegially-rewritten example, "In our example we would for example" is quite clumsy. Consider instead "In our example, one can check cache statistics with an AppFabric powershell command, but use whatever tool you most like".

Re the second example, advice to prefer readily available to easily accessible seems wrong. That a phrase is frequently used carries no weight if it's the wrong phrase. The information in question evidently is readily available, and the actual problem is it isn't easy to access without knowing all about some program.

The Macmillan Dictionary (American edition) says about cheers:

cheers, interjection : (British informal) thank you

In the US, thanks is the nearest informal equivalent. If you say "cheers" in the US, people will think you're offering a toast.

In countries that use British English, "cheers" is fine in the informal situations that you mention.

You can reserve "thank you" for more formal situations.