Is it possible to use reachable as a replacement for available? I noticed that some dictionaries don't have the former term in their database. Is there any origin for this word?
As a direct replacement, no; "we have 3 types of stew reachable," is nonsense.
There would be some cases where either could serve, but not as exact equivalents.
There are rewards available to those who work hard.
There are rewards reachable to those who work hard.
Are both close in meaning, though not exactly; both state that the rewards can be obtained, but the latter uses a metaphor of moving toward that reward and getting it, that the former does not.
Here though we've changed the imagery of the phrase, so even though they both serve, they still aren't exactly equivalent. In all, the words shouldn't be seen as even partial synonyms.
"Reachable", besides used in reference to goals, (which would not be synonymous with "available") is primarily synonymous with "available" in one context:
I am "reachable" during the day at this number: 800-555-5555
In this era of various means of communication, I actually think "reachable" is a better word choice than "available" in that context. With my cell phone glued to my hand, I am always "available" but not always "reachable" (particularly when I'm in a certain windowless room!) ;-)
The two terms don't seem interchangeable in a general context.
If something is available, it is possible to obtain in some way. The primary information here is that it exists and is not utterly obscure.
If something is reachable, it is something that you can move to. Its existence is more or less asserted and the new bit of information is that it is possible to go there from where you are now.
It might be possible to use reachable instead of available in some abstract context, but that would be quite specific. For example, you might use either reachable or available instead of attainable, but then available would sound a bit off.