Well about the soil: I don't see any big particules only a little sand here and there. The rest looks like regular dirt
Bonsai need air around their roots as much as they need water, you cant tip the scale too far in favor of one or the other without making managing it more difficult. Finely textured soils exclude air, retain a lot of moisture and take a long time to dry out. One of the primary causes of problems with potted plants is over-watering.
The water indeed flows freely when I water it and I do it according to the sticky posts here in the forum and the way you described it in your post (waiting a while and then watering it again).
OK, that is fine as far as it goes but how do you determine when to water again? One way is to get a skewer or chopstick, cut off an appropriate length and place it in your soil half way between the trunk and the rim. Leave the skewer in the pot, removing it only to check the level of moisture in the depths of the pot. Don't just rely on the condition of the soil on the surface, most of the roots are deeper. If the skewer is damp (hold it to your cheek) then don't water yet. If by chance you wait one day too long the tree will indicate this through drooping leaves, then you will have a better idea how to manage it.
I've been fertilizing every two weeks but not exactly on a tight schedule (I mean if I should fertilize on a Wednesday I might do it on a Friday, do you think that is a problem?)
That sound OK. And no the flexible schedule is nothing to be concerned about, especially with the type of soil you have. A coarse, largely inorganic, bonsai soil, unlike yours, will not retain nutrients to the same degree that a finely textured organic soil will. This means more attention must be paid to fertilizing with this type of soil.
And finally about the new location: the bonsai is in a patio, just outside a window. It is wind-protected and it as a little roof over it (actually it's more like a marquee). Lately it has been quite hot (29-30 C / 86F).
This has to be better than being inside, but you don't mention how many hours of sun, morning or afternoon, that the tree receives. I don't think 86F is anything to worry about as long as it has not dried out, which I don't think is the case.
Do you think I've been underwatering it? Or overwatering it?
From the description of yellowing leaves, organic soil and the fact that most people tend to over-water, I feel that the latter is more likely. You are in a better position to make that determination though. Has the surface of the soil ever gone dry to the touch? Or do you water it as soon as there is no obvious moisture? Try letting it go longer in between waterings. Observe it carefully, checking the soil fairly deep in the pot.
If it were mine I would definitely be re-potting it into some decent soil at the earliest appropriate time. You must use proper bonsai soil or you will have gained nothing. As far as the timing, sorry I don't grow this species and it is a bit unusual as bonsai at least here. There does not seem to be a lot of information on this species. Do some research on this species and bonsai soils in general. The sticky threads cover the basics as well as containing links to more in depth information.