How to get a crane without frightening a titmouse?

Question

Career in IT

Hello.
The story is like this. There is a company A, very famous and cool, where I initially wanted to work. I interviewed there a few months ago, but there were no vacancies for me. I regarded this as a refusal, so I began to look for other places.
It may be worth mentioning that I have no experience in IT (as opposed to desire), so I am interested in starting positions, in particular, internships.
And recently I came across an ad from company B for a two-month summer internship with the prospect of further employment. In general, I liked the company itself, although not as much as Company A. I successfully passed the selection and interview, and already as an intern developer I should go to the first working day this Monday. I mean, I'm all so happy that I got the desired position, and now, when everything seems to have settled down, a letter arrives from company A.
The bottom line is that a vacancy for an intern has opened up, and they offer me to pass the selection (they sent a task + there will most likely be another interview). In terms of time, I have 5 days (most likely I will manage before the end of the weekend) + they will check for a week. Judging by experience, they will check for _at least_ a week :). Given the interview, everything may well come out in a few weeks, or even a month. The desire to work there is still very strong.
Task: to take advantage of the opportunity from company A so that in the end I do not end up without a job at all.
In this regard, a number of questions arise:

• Should I inform HR or the team leader of company B about my relationship with A before I know the result? Perhaps this is important: I have not signed any contracts yet. It will most likely take place next week.
  
• The same thing, but in a different direction: is it worth talking about A about B?
  

Further questions depend on the answers to these.
I would appreciate any thoughts. If so, ask questions.
UPD. End of story. The interview in A went well (by the way, the interview itself was very pleasant: 2 hours flew by in a flash), but it turned out that the growth conditions at the moment are much more acceptable in B. In short, in A you need to work 40 hours a week, which will not allow for me to fully combine work with full-time studies (albeit evening ones), while in B it is easy to cut hours by almost 2 times (at least they said so) and remain in development.
Today they called from A, and I confirmed the refusal. I'll work with them later. Perhaps, by the way, I will do a project with them related to my studies.
By the way, in B I still talked about A with the personnel department (very nice women, you somehow trust them). To my surprise, they said, “Go ahead, company A is a very good company. There should be no problems with the transition, because you are still a probationary trainee.” Despite this, in general, I agree that it is better to keep relationships with other employers to yourself.
Many thanks to everyone for participating!

Answer 1

No. Your relationship with A is your business. It is better to choose from 2 than from 0.
Your career is always a bargain, so the more cards you have in your hands, the better

Answer 2

If I were you, I would assess the situation in two ways:
a) Is company B so worse than company A that it refuses to take a job?
b) What is the probability of not passing the selection / interview in A and, having two places, not getting one?

Answer 3

it is logical to work in company b and then go to work in company a