Hiho,
as with the recent Beta3 I only had limited possibility to test 'cause of the CTD after a few rounds (using Win7). After changing to WinXP-Compatibility mode I had the chance to play a bit longer (I will issue a bug report later on).
Now to my feedback and some suggestions:
Housing:
I have to admit, that the current system with gardens, and special food tiles is coming into shape and playing better with each release
With regards to the housing I would suggest to change it in that way:
City level one: hut -> lvl.2: Unlocking house possible -> lvl.3: unlocking estate possible -> lvl. 4: unlocking villa's possible -> lvl.5: unlocking mansions possible.
Whenever a player chooses that upgrade in the breakthrough and a city has the approbiate lvl the huts will be upgraded to the next level. In that way, It's not needed to demolish the huts/houses if you are building villas or mansions and you still need to decide if you invest the breakthrough into the upgrade or better in something else.
Adventure Mode
To be honest, I currently don't dwelve to much into that area currently because of the limited turns. One suggestion is, that the research of 'recruiting' should be already be a given! If I consider that I don't build a town in the beginning, I should still be able to recruit Champs with e.g. Research, Spellpoints abilities otherwise I would be stuck in that way! Additionally, in this build it seems that the 'collectables' are very rarely compared to normal resource tiles. If you are going to adventure in the beginning with an adventure type Sov you can hardly even survive the first battles. If I face 1-2 darklings they beat me to death - not really feeling as something special.
Research mode
I'm still thinking of the idea if it would not be more interesting to split available research points into the different areas. Currently I can only focus at one time into one area. As soon as it becomes to expensive or I need something else from another tree, I switch. I think it would be far more rewarding if I could divide my 'research power' into the different trees at once and gaining improvements based on my way of playing.
City Building / Improvements
There are several good suggestions already made. I want to add that in my opinion the city tiles available per City level should not be linear but a bit more progressive. The city level is measured with the people living in the city but they are not linear as well. This should be reflected accordingly.
Another point is that there should be improvements that can be placed 'unlimited' as long as enough city tiles are available (e.g. Workshop, Study centers, etc).
Afterwards you can may add some improvements where the prerequisites are a number of 'lower tech' improvements. E.g. for every 3 libraries in your kingdom you are able to build a greater library.
If I understood Frogboy right, you need to connect with your city improvements to the resource tiles if you want to harvest them by the city -> highly welcomed as well 
Magic / Shards usage
Currently once connected you can cast the spells requiring those shards. I would suggest whether to change this in the same way as other collectable resources (material, metal) - which would mean an additional micro beside the need mana (not preferable) or change the spell system to tiers requiring that for higher tier level spells you need to connect to 2 or more shards of the same type. If this is currently implemented but I don't see it because of the CTD, fine
Otherwise, may you take it into consideration.
Another point: There are some spells which increases that attack/defense rate of the caster (at least, what is told by the description). For those spells currently I have to select the tile as well to be cast onto -> To match to the description, they should be casted instantly.
UI
It's improving, but still needs some major work to be done:
Units without a champion/Sov have currently no home to be displayed or short-cut to see them. If I have to scroll around all the time on the map to find them.. not nice.
The left hand Empire-list shows currently if a city is building an improvement - but not showing if recruiting is going on. Would it be possible at least to display two small numbers to show when recruiting stack and building stack is finished? This would gain a lot of transparancy. Additionally, would it be possible to right-click on the city on the left hand empire tree to unfold/fold the current building/recruiting stack for the city?
Same should be possible for the unit/Champ/Sov icons -> righ-click showing/hiding the whole stack?
Next point: when creating a new city with the pioneer, in the window where you choose the name of the city, please additionally show the cost as a sort of reminder of the cost 
Breakthrough-Window: By left-clicking on the unlockable features you can open the book for more information. Very nice. But it would be perfect if you can click in that window for further unlocking features. E.g. If the window tells me that this improvement will unlock xy, click on xy to see what that improvement my bear 
Start a new game
I would like to see the benefits a faction has when selectng to play with those. In 2A it was there (e.g. +Farming), since 2B its more a guessing or knowing.
I hope that there will be an option to define more fine how likely tile resources are placed, how many adventure tiles are placed etc. Currently there are so many improvement tiles on the map that this is nothing special anymore.
That's for now - more to come
Open for any sort of critism 
BR
Wyl