I this case you would say "I've arrived." or "I'm here (now)." if you want to word it differently to avoid the present perfect. I placed "now" in parentheses since it is optional. :)
1-They discuss the words that have been influenced by popular culture.
The words were influenced in the past and still have that influence on them. Also, "that have been" is a passive form since the word "been" is included. An active form would be "They discuss words that popular culture has influenced."
2-I think it might have been Vanity Fair THAT used the word ‘Romneyshambles’.
Here, "might have been" expresses that the speaker doesn't know for sure who did it, so in a sense it relates to present time because the speaker is still unsure. Hmmmm. Btw, you could also say "I think it was Vanity Fair that used the word 'Romneyshambles'."
3-The prefix ‘omni’, which means everywhere or everything, has been added to the noun ‘shambles’.
Here, "has been added" means that the words were already added, hence they don't need to be and it relates to the present.
4-THIS word emphasises how really bad something has been messed up.
Something was messed up in the past and still is at the time the speaker said the sentence. :)