PRONUNCIATION TIPS: Should we really stress the "r" sound in English words?

Look at these words and try to pronounce them.

are, your, more, care, there, for, four, other, or, here, over, hour, before, higher, comfort, hear, never, etc.

Should we sound the 'r' when pronouncing these words?

Actually, there's no need for us to stress the 'r' sound let alone to sound it. It will sound awkward.
However, we sound the 'r' if one of those words is followed by a vowel (a,e,i,o,u).

Here are some tips/examples:
-"Before my eyes" - silent 'r'
 "Before I go...." - with 'r' sound
- "Hear you say" - silent 'r'
  "Here I come" - with 'r' sound
- "Four or five?" - with 'r' sound
  "Four people" - silent 'r'

Now, I've found the reason why people say that Siti Nurhaliza sounds awkward when she sings her English songs.
Anyway, I'm not perfect too as I'm still learning. Peace! :)

*Another thing, be careful when pronouncing "can't" & "can" because they contrast each other.
** "WORD" and "FIRST" - the 'r' is totally silenced.