It sounds like you did not talk to any expert about your algorithm. I also infer that you haven't read many papers in the field, since if you did, you would have some idea about how they are written and where they are published.
It may sound harsh, but if this is indeed the case, it is very likely that your algorithm is not new, or flawed, or worse than the state-of-the-art. It is not necessarily the case, but given the odds, the first thing you should do is mentally prepare for this.
Then, you should try and read as many publications in the area of your work and related ones, to try to find out whether what you did is new and worthy, trying to be impartial and fully prepared to learn that it is not. Think of it this way: if you do write a paper, it will need an introductory section explaining what's the state of art and how you improve no it, convincing enough for the editors and the referee. So this is a work you will need to do anyway.
On 2-3, it's perfectly appropriate to try and ask people for help, but I would not expect a lot out of it. For people you don't know and outside your university, the best you can hope for is to get answers to pointed questions about their area of expertise. People in your department are also unlikely to be interested if you just ask them "I have an idea outside your area, can you teach me how to write a paper out of it." They might know someone who knows the subject and re-address your questions to them, or to ask them to generally evaluate the idea, or tip you off which conference/journal to submit the paper to.
But the thing is, to efficiently ask people for help, you would need to communicate them what you did, and the only way to do it is to already have some manuscript written up.