Is it legal to make your own frontend to someone else's/government api?

Question

API

Hello. There is a regional state site. Implemented according to the scheme frontend(backbone) and backend(java). Can I legally make my frontend site optimized for phones, add some other goodies, promote, develop based on someone else's api. No descriptions of "about the site", "rules", "agreement of use", etc. no. Accordingly, there is no description and message that the api is open.
Are there any laws or regulations about the use of someone else's api, which is not explicitly said to be open (like VKontakte, for example)?
Is there any regulation on state sites, what can and cannot be done with them and their api?
Does this api fall under open data, so that I can collect statistics like a hell of a bot and not be afraid that I will be banned by ip?
Update 1:I can give an example of similar work (maybe it's not exactly the same, but let's say it would be as I describe it): there is a site \ state site for holding tenders. It would be implemented as frontend and api. And I would write down my version of the frontend and the bot (for statistics and automatic notification of a person / application). All functions associated with the bot would be paid, and the frontend would try to make it more convenient. I have a roughly similar plan for a regional service.

Answer 1

The API is there to be used.

Answer 2

Theoretically - yes.
That's right - push them your business plan and conclude a development contract.

Answer 3

In general, all this should be regulated by some kind of offer for using the site.
By default, for example, distribution of material without the consent of the copyright holder is prohibited, probably also here.