Impromptu ('mixed bag')

In each of the others, the 'voices' or parts enter one after another, in sequence, so as to maintain or build up the overall texture of the music (think of such classic examples as the rounds London's Burning or Frere Jacques; or Tallis' famous Canon, as often used for a soothing evening hymn). A Rondo has its music broken into whole sections, each lasting maybe a minute or more, one particular one of which will come back again and again with different 'episodes' between each iteration ~ in a pattern often categorised as A - B - A - C - A ... (etc)

'Impromptu' (Answer 1) is supposed to suggest 'unbidden' or 'spur-of-the-moment', but various piano pieces (particularly) by such a title are usually neatly confected beforehand to sound like a spontaneous 'trifle' or party-piece. A Rhapsody (Answer 4) may be free-flowing in form but is unlikely to be spontaneous, though it could be so in capable hands. An Arabesque (Answer 2) tends to be a piece with ornamental writing in the upper registers, notionally equivalent to the flourishes of middle-eastern Muslim calligraphy.
Extemporisation is an art practised by organists 'filling time' before services etc. although it can be raised to almost phenomenal heights. Organists such as Pierre Cochereau (late of Notre-Dame, Paris) could improvise an entire work of symphonic proportions on-the-spot from a snatch of music or scripture in a preceding service (he used to fly in by helicopter 'just' to create a concluding voluntary after Sunday morning Mass, for which some other organist had played all the 'bread-&-butter' music); your present writer heard him do just such a thing on the basis of 'a theme submitted on the back of an envelope by a member of the audience' at a gala in the Royal Albert Hall, at the console of the mighty Willis organ with its 9,999 pipes controlled from 4 manuals

These are all harps; the cultural and technical variations are quite intriguing!

Answer 1 was right, and any interested keyboard musicians can find material and layout diagrams online. Your present author once saw such an instrument in a collection many years ago, but with a perspex baffle firmly fixed over the said keyboard to deter curious fingers. The typewriter had been invented only about a decade beforehand, so the analogy probably seemed obvious ~ at least to Janko.
Answer 2 is genuine but not the work of Janko; Answer 3 is bogus, but surely there is food for thought for someone; Answer 4 is genuine, but not Janko's work either

There has been a lot of scholarly debate about this un-budgeable 'classic'. Britannia online appears breezily to discount this (accessed June 2014) while Wikipedia summarises in considerable detail a range of forensic musicological writing. Put simply, Answer 1 is not valid, and there are all sorts of stylistic, content and circumstantial pointers that the piece (under another title, or none) may have originated from another composer as a violin piece in the related key of A minor (in which key there is, for instance, a splendid violin concerto ~ which Bach transcribed for the organ, in a version which has its own splendid integrity). Most of us still think of the piece in present question as BWV 565 (a Bach work) despite such intriguing and nagging doubts; it obviously continues to 'resonate in the public ear and imagination'!

If not already familiar with this 'even sillier' version, and you don't recognise the piece from its presentation in these circumstances or format, try this link (beyond any commercials).
The piece was published in 1894 as no.7 of a series of Humoresques, in the slightly perverse and abstruse key of G♭ major (where one might have expected a simpler tonality; but perhaps all those black keys somehow add to the charm of playing it).
The link to the words is explained, with a strange mixture of relish and scholarly detachment, on Wikipedia ~ should you wish to confirm its genesis by searching on the composer and piece title. They also remark that the piece is possibly second in popularity only to Beethoven's Fűr Elise as a standard salon solo.
Dvorak had meanwhile been a keen train-spotter since the age of 9 in and around his native Prague, and on one later occasion is alleged to have scolded (or even sacked) a manservant that he had sent 'by proxy' to spot some train or other at the local terminus, and who came back with a wrong rolling-stock number faithfully recorded in his notebook!

The HQ of the British Folk Song Society is named in his honour. The name (though quite coincidentally) does powerfully evoke cross-country research in raw weather, a mental quickness and initiative, and a kinship with the keys favouring open strings on the fiddle

The whole suite is splendidly atmospheric, illustrative and accessible, but this early statement of its links with everyday culture is a clear and positive element in that successful appeal. Well worth a listen, whether or not you already know it!

'415' is the magic figure; very cosy if assembling for a rehearsal after a cup of afternoon tea

'Bis!' (if expressed forcefully enough, perhaps with a little lingering hiss) is usually cue enough