[Xperia Z1 Compact Q&A, Help & Troubleshooting] Coirpre:
1. How harmful is it to root, unlock bootloader etc?.. I would imagine it is no different than Jailbreaking.

Rooting is a bit more work than jailbreaking, because no simple one-click-method esists anymore/yet/at the moment. A rooted device allows you to modify EVERYTHING there is on your device (software wise). This naturally brings some dangers, such as losing all your data, or bricking it. As the posters above already stated, it is quite hard to do lasting damage to your phone. Overclocking and removing overheat protection might, but other than software-induced hardware damage, it is nearly imposible. Keep in mid that playing with partitions might require you to open the device to repair the software.

Additionally, rooting via Bootloader unlocking* removes Sony's DRM-Keys. This mainly stops Xreality and the Bionz image processor from working. it is possible to back up those keys, and i would recomend doing that. It complicates rooting a lot, but makes it possible to go back to a 100% stock phone if you ever want to. they are located in their own partition (TA). flashing another TA partition than your own will also cause your phone to be permanently broken.

2. Am I able to store absolutely everything on the SD card when it comes to applications and tweaks?

You should be able to, yes. I am however not sure how you mean that. Some tweaks like init.d scripts need to be in the system folder, as have some of the apps. It is certainly possible to have them elsewhere, but it will require some effort. Why do you want to have everything on the external memory?

3. Is it possible to remap the physical buttons to do other things?

Yes.

4. I have came across Cyanogen quite a lot, is it stable and will I notice any speed issues compared to stock OS?

CM is stable, yes. they have "Snapshot" builds, which are lightly quality tested (boots, features work as they should in most usecases, etc) and nightlies. Nightlies are builds that are generated automatically every night by a bot (3 actually) and are also quite stable. But it can happen that there are mayor bugs (not booting, stuff crashing left, right and center...), specially at the beginning of merging a nes Android release. rolling back to the last working FW will normally fix that.

Speed is normally faster because it has less bloatware.

5. Is there a "Tweak store" of sorts to download all the extra stuff after rooting the device, similar to "Cydia" for iDevices?

No. You have t find it yourself and sideloas the *.apk. Be careful with what you install. Stuff on the forum should be fine, because other able coders quite quickly raise awareness if something's not right. For Xposed there is a dedicated repo which you can access from the module itself.

there are so many versions of Android and rooting tools for individual devices!

This is the reason why there are device specific forums. Stay here for everything device-related. There are special forums for non-device-specific stuff as apps and certain tweaks.

I hope this celaned up some questions, if you still have some: read, read, read! learn, and do not be hasty in the beginning. Or just ask me...

oh, and:

This can in no way be generalized like that. tastes are different, and everyone should decide by themselves.