Wow, I perfectly understood the whole of your Portuguese text, except for saúde. Thanks Duo and thank you all native speakers and non-native speakers, who comment and help us a lot ;)

Let me try to edit your English:

In this case, ''andar/caminhar com o rei'' are the same [thing] (or "is the same [thing] as «something»), but in others contexts they have differences. I will to try show you the difference(s) between these words.

''Andar'' is what we do every day. We walk (andamos) to go to the market, for example.

''Caminhar'' is an exercise. ''Caminhar'' is to walk for a long time, not to arrive at a certain place, but for example, for health reasons.

If you are to write (or just "you write") in google ("on" should be fine too, but not "the google", unless it's an adjective as in "the google search") the word ''caminhar'', many health sites will appear.

If you mean a specific time, you should use past simple, but if you mean general action with a result valid at present moment you should use present perfect:

• I've made many mistakes (general, present perfect)
• I made many mistakes, when I wrote this (specific, past simple)

Also note that adverbs (probably) usually go after the subject (I) and auxiliary verb (have), but before the main verb (made):

• I've probably made
• I probably made

I thought maybe it's some known phrase?...