He almost certainly was using the same Bitcoin node/wallet software that he released for everyone else to use
He had to use a bit different version in some cases, for example to mine the Genesis Block. It could be almost the same code, but some little changes here and there were needed to make it, but of course after doing first steps he could start using the same version to check if everything works as he planned.
Why would he create a strong and secure miner/node/wallet for everyone else, and then create a separate less secure miner/node/wallet for his own use?
Less secure versions were first, then more secure versions were created. For example, in pre-release version the difficulty for testing was set to 20 bits for testnet and 40 bits for mainnet. That may be also the reason why the Genesis Block meets 40-bit difficulty. It is quite unlikely to hit that low block hash and not hit any 32-bit hashes first, but it has to be confirmed by re-mining.
If he did create a separate miner/node/wallet software that used non-random keys, then why wouldn't he have released that software for others?
Because it could be present in pre-release testnet, but removed in mainnet. If you test something, you need some workarounds to check things quick, for example lower difficulty. You could also need easier keys in some cases, it depends on your tests.
Why would Satoshi want you to grope their money?
I doubt he wanted it. Maybe it was needed in testnet, but in mainnet there was no reason to make that system insecure. But it had some holes, for example "OP_TRUE OP_RETURN" or Value Overflow Incident. Every software has bugs, but if Satoshi just used random keys from OpenSSL, it is unlikely that his keys are non-random. It seems he didn't know even about key compression or DER signature encoding. Also note that setting non-random ECDSA key was not that easy in OpenSSL, so I doubt there are any non-random early keys.
You needed to download the source code and compile it yourself.
For non-programmers it was the case, but as a developer, he constantly wanted to improve his software, fix bugs, etc. So there probably were some cases when he was trying to test something and used some different version before making next release. Also, it is quite likely he used his testnet with 20-bit difficulty just to double-check things before releasing that to the public, he said he wrote some code first, then wrote the whitepaper, and then published pre-release version, and finally the first official version with the currently existing Genesis Block. It is quite likely he did that many times, not just once before "setting things in stone".
But his-her-their version had some features
There definitely were some features, for example in "market.cpp" file, where Satoshi tried to do some eBay-like P2P market, also notice the code for poker game that was in the first release. So he definitely tried to do some things that were not active in the official version, there are some traces of that, because he probably forgot to remove them before making a release.
Satoshi could have set the rules so or run lots of hardware, that they mined 99% and we 1%. But didn't do it. Why?
Because that kind of system would be unfair and people would go somewhere else. Today you can see many projects with premine or where developers can decide about a lot of things, just because they want. Trying to get people attention was difficult, because Bitcoin was a very inefficient solution to the double-spending problem. People thought that there must exist some kind of system, where things are similar like in centralized systems, where you can simply remove old transactions after some time, where you don't have to know about everything what happened in the whole network. When you read the whitepaper and have performance in mind, you can easily think for the first time that this kind of solution is the worst you have ever seen and simply cannot be used in practice.
In my opinion it would be unfair ''from their serious attitude towards the project'' to mine coins, mark them and let them unmoved, if that was their intention.
That's why the owner of around one million BTC is called Patoshi and not Satoshi. I don't see any connection between Patoshi and Satoshi, so far it is not clear if that's the same person or not.
So, to sum up: I think that Satoshi's keys are random, but he probably used some different versions, just to test things, bootstrap things (the Genesis Block), test new features, and so on.
