I want to point out that while Swedish has this construction that English doesn't have, there's also an English construction that cannot be used in Swedish:
The Museum opens from 10am to 5.30pm every Tuesday – Sunday
We can't say that with the present tense of the verb öppnar in Swedish. It would have to be museet har öppet or museet är öppet. In Swedish, when museet öppnar, that is something that happens at a point in time. It cannot be stretched out in time from 10am to 5.30.
So you can say Museet öppnar klockan 10 = The museum opens at 10, but that only refers to the point in time when it opens. After that, it is open (det är öppet or det har öppet).
Yes, both those work, except I'd say från 10 till 5 – I think people disagree about whether "tills" is wrong in this context or not, but till is overwhelmingly more common and also what would traditionally be considered correct (tills is historically a contraction of till dess so it basically means 'until [that]'.) – in many contexts both are used, but between two figures like this, till is preferred by most.
No, öppen needs to have the same gender and number as its main word, so that would be de är öppna. That's a possible sentence, but note that we don't use it the same way you can say They're open in English – for instance to say that a store is open. To say that, we must say De har öppet. If you are speaking about several objects of people though, de är öppna works. Like, question: Are the windows open or closed? Answer: De är öppna.
Att öppna, öppnar, öppnade, har öppnat - is the verb (in infinitive, present, past and perfect present tenses respectively). Verbs do not change with singular/definite/plural.
Öppen is an adjective. Adjectives do change in the manner you describe. Öppen, öppet, öppna
eg. En word: Dörren är öppen
Ett word: Barnet är öppet (open can also be used to describe a personal characteristic much like in English.)
Plural: Dörrar är öppna.
Definite (double definite form): Den öppna dörren
Like others on this page, I also wanted to use "ar" instead of "har." So, let me ask a related question. If you were asking a store owner if his store is open on Sundays, would you say "Ar du oppen pa sondagar" or would it be "Har du oppen pa sondagar?" OH, and of course I didn't use the accents because they aren't available .......