Instead of "Hold on a second", I would use "Just a moment please" or "I am just going to put you on hold for a moment".
"Thanks for waiting" or "Thank you for holding" are fine.
With your second question, I think the main reason they may not understand is the same reason I don't - what does "I need to port in a customer's number" mean? It's not a phrase/phrasal verb I've ever heard and I can't work out what it might mean even from the context of your post.
You should say "I have a customer on the line..." - that makes it clear it's the telephone. If you say "I have a customer on line" it sounds like "online", meaning "on the internet".
I don't think there's anything wrong with "Let me transfer the customer [over]" if you're talking to another department within customer services or within your company. You would say to the customer "I'm going to transfer you to [name/department] now. Thanks for your call" or something similar.
Also, review your spelling of "either" (it's not "eighter").