There is no "spoofing" or "manipulation" or "bypassing", it's simply sending a packet to the address and a router doing what a router does, in a use case that simply doesn't involve the NAT.

The idea that NAT prevents inbound connections is simply a myth believed by tons of people who have no clue how IP works. It simply doesn't. So you don't need to do any "spoofing" or "manipulation" to "bypass" something that NAT simply doesn't do.

You might as well say that you can bypass a P.O. box by spoofing the destination address and thus effectively manipulating the snail mail routing. No, it's simply the case that you can address letters to street addresses and the postal service will deliver them to the address written on the envelope. Your mistake is in the completely baseless assumption that a P.O. box is supposed to prevent letters from being delivered to your street address.

Then why is it necessary to Port Forward / have an Open NAT in order to connect remotely in most cases such as online gaming or ssh?

Because the internet generally does not route RFC1918 addresses, and in particular not to you. But that is not a security feature, as there is no guarantee that noone will ever send such packets to you, it's simply that those addresses are not (uniquely) allocated to you, and therefore, your ISP doesn't know to route them to you. Also, many ISPs won't accept routes for RFC1918 addresses from other ISPs because it is well-known that they are not allocated to any particular party, and anyone announcing them risks being flooded with packets leaking from local networks that cannot usefully be delivered anyhow.

But nothing prevents your ISP from sending you packets addressed to RFC1918 addresses. Or anyone who happens to have compromised your ISP('s router), for that matter. Also, it happens that ISPs fail to properly isolate customers, and neighbours who are customers of the same ISP can directly send layer 2 packets to your router. Or it happens that ISPs forget to disable routing protocols on customer-facing ports, and if your router is misconfigured as well, it might be announcing your RFC1918 prefix to your ISP, which then would start routing packets from its other customers addressed to that prefix to you (probably not from other ISPs, as BGP peers usually would drop such routes--but even that is not guaranteed).

It's just a convention to not route RFC1918 addresses over the public internet for the simple reason that they are well-known to not belong to anyone in particular, and in any case your ISP generally wouldn't know who of the many users of those addresses to deliver packets to. I guess that's a bit analogous to writing "to Joe by the big tree" on an envelope and dropping it in the mailbox. That is not a clear, unambiguous address, belonging to one particular person, so chances are the postal service won't know what to do with it and it won't ever arrive. But that doesn't mean there is a guarantee that it won't arrive. Some postal worker might happen to know Joe and that he is known in some circles as Joe by the big tree, and the letter might arrive after all.

That is PAT not NAT. Port numbers are a scarce resource and there are various ways to allocate them. This may be a 1:1 or 1:random or n:n static range or n:n random.

A stateful PAT would inspect packets to set up port translation and these things used to have lots of bugs and no filtering to check if the packet is from internal or external network at times.

You can often still send to the direct target port and IP if you guess or figure out the mapping. Scanning 64k numbers with packets is not that hard.

Because you can't route a packet addressed to 10.x.x.x or 192.168.x.x or other private network spaces directly over the Internet, which is the attack people are talking about here.