Hi @Henrik_Roksvaag ! Welcome to openHAB 
Everything you asked for is certainly possible with OH, as it really just acts as a gateway, and as long as a binding implements a functionality, it’s available for you to access/modify with one of the many openHAB administrative/client UIs, rules, etc…
I can give you some basic pointers and ideas for most of the questions you asked, and I’m sure there will be others who can provide more in-depth information on each topic. You certainly seem to already have great HA experience, so it should be fairly easy for you to bring everything over, as soon as you get familiar with the many ways to configure or do things in openHAB.
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The best way I can think of handling state-based actions is storage items, and making your own scenes based on the currently selected “mode”. I wrote up/made a video about this: 3 different methods to use scenes with Google Home & openHAB
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Correct, HABmin is the best tool I know of to make ZWave configuration changes. Add all devices as Things using PaperUI, then open HABmin.
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You can make rules as advanced as you want, and there are probably hundreds of different ways to do this. One I can think of quickly would be a cron-based rule that fires at 0700, and sets an item state (e.g. MorningTime) to ON. On the item definition, use the expire binding to set it back OFF after 30 minutes. Of course, you don’t need to do it that way, you can also check the current time in the rule you fire when the motion sensor goes off. BTW, this is a great idea (playing music on motion in the bathroom only at certain time) - I’m stealing it
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You could probably implement this the same way you have it done in FutureHome, or implement some presence-based rule.
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I’m not too familiar/don’t use TTS at this point, but I know TTS with Google Home is available, so it should absolutely be doable in openHAB.
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For presence detection, you could use your phone/connection to Wifi (check out this blog post)
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Definitely lots of options as you said. You can implement them all if you implement my scenes/routines setup I linked to above (i.e. fire the scene switch using Google Home, or an external pushbutton, or the UI, or based on a time-based rule)…
As I said above, the options are endless and I’m sure you’ll find that as you implement things one way, a new way will become visible (and like all of us, you’ll end up refining your setup as you go)…
Once again, welcome to the forum, and good luck!