Tier 1 Village improvements worth doing AFTER liberation?

So my understanding is that T1 Village improvements do not cost construction points and can be built prior to liberating a town. Those items will raise your trust level with that town.

T2 Village improvements will cost construction points and raise the towns prosperity level.

I believe you start with some number of construction points which is enough to build the scout stand and the village house. More points can be gained by raising prosperity or demolishing building the village self invested in.

More T2 improvements I guess come from advancing to T3 on your own village.

My questions are...is all of the above accurate? and is there any point to placing T1 Village Improvements after the place has been liberated. I googled the second question and the AI answer said they were important to place but then continued on to describe the scout camp and house as T1, which they aren't.

I don't want to waste time/resources continuing to build these if they no longer help. The second city we liberated got to protectorate before we even built a single T1 Village Improvement.