You can enter anytime within the 5 year period, BUT, the website says you shouldn't apply (yet) if your intented entry date is beyond 90 days in the future. You have to write the date when applying, so you would need to willingly lie, which is not recommended.
each application is processed and granted by a different Embbasy. Each one has very different rules and requirements, not only in relation to medical appointments. For example, some demand you have had the money for xx months. Some, notably Malaysia, demands you to have a long term (at least 6 months) lease in Thailand, or they won't grant the visa. Some demand you to be a resident of the country you're applying at, etc.
It has not much logical sense, but it is the way it is. A single few weeks course or a single medical appointment has been enough for some people to get the DTV. It seems they're becoming a bit stricter over time, tho.
I applied in Seoul, Korea with a Costa Rica passport issued in Seoul. My passport says Place of issue: Seul (which is is Spanish language for Seoul). On my application I wrote "Seoul" and it was approved.