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All four are fixed and the build is up.

The twigs: past zone 8 the loot switches to the next resource, but twigs stay the main part of every recipe, so you could get stuck exactly as you describe. There are now two buttons next to the zone name that send you back to any zone you have already reached, and the game picks the highest wave you can still win there.

The two second freeze: every purchase redrew the whole nest even when nothing about it had changed. It only changes one purchase in eight, so seven clicks out of eight are instant now. The eighth still costs a moment.

The save: there was none at all, and I am sorry about your hours. It saves after every purchase, foray and rebirth, and there is a SAVE button in the top right that also lights up when the game saves on its own.

And the nest: you were right that it did nothing. Chambers now have a job you choose, brood, granary, infirmary or fungus farm, and each is worth an upgrade level. That is a start rather than the whole answer. Thanks for writing all of it down.