[Sony Xperia XZ1 Compact Guides, News, & Discussion] tonsofquestions:
Hi and welcome! That's a lot of questions - and a lot of very subjective information. I'll try my best to answer where I can. For context, I still use mine as my daily driver.

Performance: That all depends on what you want to do. Can it handle the most demanding modern games? Probably not, but what do you really want to play? It's a compact phone that's 5 years old. It wasn't the strongest for games at the time. Can it run most apps just fine? Yes. I've not run into much that have a problem, but I'm also not doing anything too intense, and I know that. Of course, phone processors have largely been commoditized by now, despite what manufacturers would like you to believe.

Battery: Again, it's all about what you do with it. What are you running? It of course won't last the whole day playing video with the screen on full brightness. But no phone will. Battery is more tied to screen size than anything else. Your particular mileage may vary depending on whether your device is used, and how well the previous owner treated it in terms of charge cycles and limiting. Mine easily lasts a day, but I don't tend to use it super heavily. Draining quickly is usually a sign of greedy apps or a busted battery.

Camera: I don't personally have strong opinions on cameras, so can't really comment on whether you like the quality - people have very different requirements. It's perfectly adequate for my needs. Will it be as good as modern phone cameras? Certainly not. Most modern phones have multiple sensors with different kinds of lenses - which drastically changes what's possible. Do you care about that? Only you can answer.

Stock Software. I can say with 99.999% certainty that Sony is never going to release an official update. Don't hold your breath. It's 5 years old, and very outdated. I don't believe there are any more security updates, and again do not expect any.

Custom Software: Let's be 100% clear. There's a locked bootloader, that you have the ability to unlock - but not re-lock. If you don't unlock it, you cannot install a custom rom. Full stop. That's the case for every phone. If you unlock it ... then you can do whatever you want. There are many custom roms available (check out that subforum here), including to the most recent version of Android 13 (via Lineage OS 20). But you'll have to do a little bit of work. If you do unlock it, I recommend doing the pre-work to back up your TA partition, since it will help a little with the camera should you decide to go back to stock.

Alternatives: Again, lots of opinion here. What do you define as "compact"? I'd argue that there are no comparable modern phones that are anywhere near this size, other than the iPhone mini ... and I don't like Apple/iOS. Maybe you don't mind that. Maybe you're willing to go up an inch in screen size, and that's still small enough for you. It also depends on what other features you need/want - like a SD card slot, headphone jack, 5G, etc. To me, there's nothing better, which is why I still use my XZ1c. I know other people that swear by some of the Pixels, Zenphones, or even a few of the smaller Samsung phones.

Finally, you mention the DOCOMO SO-02K version. I don't know where you live, but it runs different firmware (Japanese) and a different set of apps. I think the OS version is even older, and has fewer updates. It's missing NFC (and I think some other sensor), and some of the wireless bands. And as you say cannot be unlocked - though I vaguely recall a post of someone saying they were able to.

Unless you know what you're doing, I would not advise getting that version. The standard G8441 version is a better and more flexible buy unless you live in Japan (and are OK with the lock) or know what you're doing. If you're serious about the phone, it's worth paying a little extra to be sure about what you're getting.

I hope that helps! And remember that this is all just the opinion of one member, but I've at least tired to be as impartial as I can.