Those are very interesting questions, here are my thoughts for what they are worth.
1. Does the best poetry come from hard work and discipline? Is writing poetry just a process?
I believe poetry like all art forms is a discipline, something that needs to be worked on in order to improve.
I have been writing for almost six years, at the start I wrote a lot more poetry than I do now. I was learning and experimenting, finding my own voice. With each new poem I try my style of writing, I hope, should be refining itself.
No I don't think it is a process, as far as I can work out there is no "special" method to writing poetry. If there is a twelve-step guide I would to know about it. I tend to write free verse or style. It is a personal choice. I have no desire to try some more constricting like a sonnet, as I am aware of my weaknesses,
And I don't think my thought process would suit those styles and techniques. I just write about what inspires me, what engages me.
2. Or does beautiful poetry come from writing inspired? Can poetry be written within that short span where a person is completely immersed in his/her topic?
All writing comes from being inspired, whether it is from something internal (a first hand experience, an emotion you feel) or maybe by something you witnessed or a topic you have an interest in but have not witnessed first hand. Personally I think outside influences are essential otherwise you limit yourself in what you can write if you only write about first hand experiences. By the second part of the question do you mean the part where you hit upon an idea for a poem and the whole thing seems to come together instantly? That rarely happens with me, when it does I never seem to have a pen. I have written few poems in a one sitting where they remained in first draft form. Some poems I will edit about six or seven times. I think most poems are written in several sittings, each time you come to the poem with sometime new to add, it is almost like a collage of emotions with a central theme. Poetry is a very concise form so often whole images and emotions are compacted into five words.
3. I believe that poetry should be inspired, but is that wrong thinking? Is poetry too complex an art to "freestyle"? Are there poets out there who "freestyle" poems?
Free style… meaning without any verse structure such as stanzas, haiku form or sonnet form?
Well I would say that my poetry is free style though over the past I have started writing poems with equal amount of lines in each verse. It is not sometime that I set out to do intentionally, but it is possible to put some sort of structure to the poem I do. I think the only bad poetry is poetry that does not come from the heart that is full of clichés that lacks honesty. If you search deep inside yourself you can produce beautiful words, the images do not need to be complex as long as the emotions are true and can connect with people.