That throws me off how close câștigătoare is to the Spanish castigar, to punish. I wonder if there's any relation.
a construi = to build
construcție = building
construit = built
constructor = builder
Of course one can construct a plan, an argument or a strategy as well as building one and to construct in English means to build so DL should allow this - but it isn't even offering my answer should be accepted today.
câștigătoare is the female of "winner", right? can it be used both as a substantive and as an adjective? grammaticaly, it is an adjective, right?
When are we going to be able to use the present continuous form for the English sentences? "I am building" is much more natural in English than "I build". Is there a distinction in Romanian between present simple and present continuous?
There is no distinction in Romanian between present simple and present continuous, but if you wanted to use something more along the lines of the present continuous, you could say "Sunt în procesul de a construi o strategie câștigătoare." = "I am in the process of building a winning strategy." It's a bit less direct and more involved, but definitely doable.
There is no distinction between the present simple and continuous in Romanian, so a sentence like this could almost always be translated either way depending on the context. So you should be able to use the English continuous tense here. If you can't, you should report it.