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For some reason on Constructor I am being limited building some houses or undesirables. Usually the max for each house is 5, however I often get to build just 1, 2 or 3.
The last quest (to build 4 houses of same kind on a territory) I could not beat it because I could not have 4 of them, just 3 (and no, I did not have any other of same kind built). Also sometimes even if I have built 5 houses, but I decide to demolish 1 and rebuild it, game tells me it is not avaiable.

And for workers, late game when I have many workers groups around but I want get some gangsters, I end up seeing that I have 5 workers on my HQ and when I click on it the HQ tells me I have just 1; and I get punishments from the Council.

Am I missing something with these two problems?
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The problem is that your enemies have built their own houses of the same type. If they ask you to build, say, four Mock Tudors and your enemies have a lot of them then you'll need to destroy some.

If I remember correctly... Each team gets at least one house of each type. (So at level 4, that's one Mock Tudor, one Scottish Lodge and one Town House.)
Beyond that, 4 more buildings of the same type may exist, shared between the teams based on who gets there first.

So in this case the solution to your problem is to find out which of the other team has more than one of the house you need and blow up their excess so you can meet your mission requirement.

As to your second problem, I don't quite understand what you're saying, but I do remember there's a limit on how many workers you can have before the council starts fining you. Just ask your level 1 tenants to stop breeding them until you need to replace them.