Budget is important but not a 100% essential ingredient for a startup. You should consider employing some of the lean methodologies if you want to optimize on the budget you have .
Startups which deal with information management typically require intellectual capability more than financial muscle. So you can consider starting an internet related startup.
Similarly selling on-line helps you to minimize the marketing costs as you can reach out to initial critical mass using various social media channels/forums to get going.

I would love to have a call with detailed guidance on each of the sub-questions.