There is no port in for ISPs as you will be giving with new set of fixed line number, account etc. Only new application and termination.
Yes, you will still need to apply like normal and the agent will mark that you are an existing user for X ISP which your current ISP will be informed.

Also yes, if the current provider counter-offers you and you want to stay with them, you can reject the new provider's application. Usually, the current provider will help you to reject the new provider. You can inform them to do it for you.