The forte symbol: f means "loud", but it doesn't mean just play that note loudly; successive notes after this symbol should also be played loudly, (until another dynamic symbol is encountered).
The marcato symbol: ^ means "marked" or accented. This symbol only effects the notes it is on, and successive notes should not be accented.
The sforzando symbol: ...
It can be sometimes that music which is unfamiliar to us in style doesn't sound like "music". What "sounds like music" to people is often that which is familiar to them, and often in a style that they heard a lot when quite young.
(When I was young I became a jazz fan by listening to older style artists like Louis Armstrong and Count Basie - but the first ...
The best way to record an instrument like this is by using the line-level outputs. Connect these to your computer via an audio interface (a 2-channel interface does not need to be expensive, you can get a basic one for less than $30).
I actually have the same keyboard, and it seems off that you don't think it's loud at max volume. I play with an 1/4" headphone jack plugged into the front port and I can't turn it up more than halfway or it starts to hurt... You're not trying to plug in an 1/8" jack into there without an adapter or something, are you? Can you try with another pair of ...
Marcato is an emphasis. Particularly on longer notes, it's very much like a sfz in that the note reverts to the current dynamic level after the initial emphasis.
Forte, in the absence of crescendo/decrescendo marks, indicates a constant sound level for the entire note (as well as all notes following until other markings appear).
Marcato can be played with a dynamic of a p (piano). As you say it is an accent relative to other notes in the same, previous or following bars.
Forte is depending of the velocity of the attack so it implies for keyboards somehow an marcato, but with other instruments (strings, woodwind and brass) you can play forte with more or less marcato.
Yiruma is the 'River flows in you' guy? Sure, you can have lots of fun playing in that style. But, as you've discovered, that's just one small area of what a piano can do. If the dramatics of Beethoven or Chopin don't attract you, how about Debussy?
Or the elegant simplicity of Mozart?