With my current ISP, I have a static IP address for the server to be able to access it from anywhere in the world. Now I'm changing ISPs - should I ask a new ISP for new static IP address, or can I reuse the current one?
Unless you have your own provider-independent block of addresses, you will not be able to take your addresses with you.
ISP will not advertise prefixes longer than
/24 for IPv4 or
/48 for IPv6. That means if your block of addresses is smaller than those, the IP addresses are assigned to the ISP, not to you. A new ISP cannot advertise your address block if it belongs to your former ISP.