Yeah, you'll need a public IP. Are you sure you don't have one already? Who is your internet provider? What broadband active connection do you already have?

Because you are given private IP, like mobile internet fromndogo/maxis/celcom all are private IP.

So far I know only unifi  give public IP by default

Service provider like TM has to apply to a world body for a range of IP addresses.. When Internet was created they thought will not run out but the addresses do run out. That is why now world migrates to IPv6 for more IP addresses.

So when your modem or BTU Broadband Termination Unit is case of fiber) is connected to Internet, the IP address the unit were assigned a public IP address. Then it goes to you wireless AP and the wireless AP generates private IP addresses for devices in your local LAN. The gateway for your modem or BTU is public IP address.

Therefore, when you want to connect to your house, you connect to the public IP address assigned to your home. The same was the websites you connected to www.blah-blah.com is actually a public IP address.

However, since TM have limited public IP addresses, TM has used a router at its node and the customers get private IP address on their modem (most Streamyx customers). The Unifi customer I think still get public IP address. What about service providers that use TM fiber line service. They are given even less public IP addresses. Theregore many of their end customers get private IP addresses. Those on company subscription or persons that need to have public IP address has to request and probably pay more. This is another reason company pay more.

However, there are other condition. Home user get Dynamic IP addresses though it is public IP address. Every time you connect to the service, the public IP address is assigned randomly. So, for company, they would want fixed IP address to enable anyone who access its website. If your home IP address changes all the time, you are unable to log in to your CCTV remotely.

However, there are other service that provide access even if you have dynamic IP address.

It's possible. Some DVRs call this P2P. Look at the DVR's config. See if there's something called P2P, some have a QR code which you scan with the smartphone app. You don't need a public IP for this. A 3rd party server is used to establish a connection from your phone to the DVR. Technically it's called a UDP hole punch. Some call it reverse port forwarding which is a totally made-up term but hey, as long as it works. What brand is your DVR?.

Your Aztech is using the same thing.

Here's a video on Youtube. Hopefully your DVR has this feature.

Yes, not possible with private IP address because there is no way you can type your house IP address to access your CCTV. Private IP address is just local IP address that can be the same duplicate address in other local LAN. Only public IP address unique to everyone in this world.

Another thing is that your public IP address has to be fixed. If it is randomly changed from time to time, then you are unable to know what is your IP address from remote location.