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.

Recently, my uncle's Maxis connection at our family's old house had issues due to Tropical Storm Senyar, and the cable broke. Then, only did we find out it is an Allo infra and not TM. So Allo contractor came to fix it, and they asked us to install Allo instead. I just checked it is only RM 49 for 100Mbps oh wow. Looks like we will switch to Allo once this contract ends. Moreover, we don't need to wait for Maxis to send Allo to fix it. This time, they took two days to fix it after numerous follow-ups.