It's a surprisingly old usage. Here's one from 1786 saying a sum of money is to the tune of two millions and a half. Coincidentally, I'm just watching the 1962 remake of Mutiny On The Bounty, where Captain Bligh says it matters to the tune of £1000 a day that breadfruit should arrive in Jamaica as soon as possible. It's set in 1787, so Hollywood got the speech of the times right there.
TheFreeDictionary: tune definition 2 has...
- a. Concord or agreement; harmony: in tune with the times.
- b. Archaic Frame of mind; disposition.
I think both those two senses, paricularly the latter, would have made it barely even metaphorical to use "to the tune of" for "about like that" or "of that ilk". Maybe someone can track down a "first recorded use", but I doubt that would represent the coining of the expression.
I suspect shifts in the meaning of "tune" have led to the current situation where OP is not alone in thinking the expression seems a little odd. So now it's thought of as an idiom, we continue to use it for money but don't feel comfortable transferring the meaning to other contexts.
LATER: Here's a usage from 1738 writing of a publication containing 9764 "Questions & Answers" (an early precursor to EL&U!), in which the author mentions an earlier publication with "to the tune of Nine Hundred [Answers]". The referent isn't/wasn't always a sum of money.
Some of your questions are answered by this website, which contains a transcription of the original pamphlet describing biritch. Collison (the author of the pamphlet, and a railroad engineer who worked for a time in Turkey) apparently wrote a letter to The Saturday Review dated 28 May 1906, where he describes the history of the game. I quote:
Between 1880-4 I spent a considerable time in Constantinople and Asia Minor, where I played what was then called 'Biritch or Russian Whist'. I was then living, while in England, at Cromwell Road and introduced the game to many of my English friends, who liked it so much that they asked me to have the rules printed. ... 'Biritch' was attributed to the Russian colony at Constantinople; in my time the dominating social and political element. [not my ellipses, but the website's]
There were many variations of whist played in Russia, which this game was similar to. Mari-Lou in the comments has found a source that showing biritch is a variation of an earlier Russian game called yeralash. So while it's not clear whether the word biritch was originally Russian, most of the rules of the game are.
The word "biritch" means (in the game) no trump, although it is unclear whether this meaning is connected to its etymology. Maybe somebody who knows Turkish could tell us whether biritch might be a Russian mispronunciation of some word or phrase meaning "no trump".
More information probably can be found in the original version of The Saturday Review letter and also in another reference given on the above website: Thierry Depaulis and Jac Fuchs, "First Steps of Bridge in the West: Collinson's 'Biritch'", The Playing-Card, Vol. 32, no. 2, Sep.-Oct. 2003, pp. 67-76. Unfortunately, I can find neither of these online.
Best Answer
There is also the usage "ramp down" in addition to "ramp up"
I think the definition of a ramp as an inclined slope is what is in use in both cases. If the slope inclines upwards, it's "ramping up" and signifies an increase in whatever is being measured. Similarly for "ramping down"
Etymonline for ramp also identifies it as a slope.
Note: This also says
which is what @Annarita's answer has
However, the usage for a creeping plant I find is not "ramped up" but just "ramped"