Well potting soil is not a very good soil for bonsai, and unfortunately, thats what most come with when you buy them, because its cheaper than a good quality bonsai soil. It holds far too much moisture though, which will cause root rot or fungus, and unlike a tree in nature, a bonsai tree is not able to outgrow problems like that. So good soil is very important. Also, if soil covers some of the trunk, you can just get rid of that, so it doesnt slope, and because having the trunk under the soil can cause a whole other set of problems. That should help the water absorb better, so that you don't have to soak it, which is especially dangerous with regular potting soil because it holds so much water to begin with. It sounds like the soil is in good condition though if it is still dark and rich looking, and if the water absorb quickly (even if not quite quick enough with the slope). when the soil stays clumped, thats probably just because its not a good mix for bonsai. Potting soil clumps pretty easily with all the organic matter in it, plus if you are doing this shortly after watering, the water wont help it stay loose and crumbly. Either way, it sounds kind of like you've got a big clump of dirt that your tree is growing in, which is not really ideal at all. If the tree was growing well, then thats good, but obviously if it has a dead branch something is wrong (though I'm not sure it would be mineral deposits from the way you describe the soil). But keeping the tree in potting soil is a big risk.
I've never encountered a trunk just splitting before (unless of course it was dropped or something, but it doesnt sound like thats the case), so I'm not sure about that. Some trees wil grow slower than others though, and many slow down a good bit in summer and especially in fall, so that may not be too concerning (a split in the trunk on the other hand 8c\...).
A good basic bonsai mix that will work for most trees out there is one that is 75% inorganic and 25% organic. Some of the more avid bonsaiers out there insist that no organic material is necessary, but for a lot of people (myself included) its hard to imagine growing plants without atleast a little actual soil.
Its probably easiest and cheapest to make your own. There are many options for the inorganic portion of the soil. A lot of the time what people use will vary by where they are. but some common things to use are pumice, lava rock, turface, chicken grit, perlite, vermiculite, and even proken unglazed pottery. Most of these will be available at a garden shop, the chicken grit can be found at feed stores, or for the pottery you can buy cheap untreated terra cotta pots or find a pottery studio and ask them about pieces that have broken or exploded during their bisque firing. All these materials have different properties, and some people like to use a mixture of more than one to get the properties they want, while others do fine with just one type of inorganic. The use of things like perlite, vermiculite, and fired clays will help reduce the amount of organic matter that you need because they hold a large amount of water but are still very free draining (especially clay).
For organic material, a lot of people use peat moss, but personally I am not a big fan. It can be very difficult to rewet once it dries. A lot of people use bark (pine or fir seem to be popular), leaf mulch, even sawdust. don't use garden compost or manure as they often carry bacteria that can harm or kill your tree and in many cases are too nutrient rich and will burn the tree. All mixes need to be sifted before they are used to prevent clogging the screens and causing exces water retention. Generally, people will sift to remove anything under 2 mm.
Different trees have different requirements for what they need. Fruit trees normally need to be kept a little more wet than say a juniper, so a good bit of vermiculite, perlite, or fired clay will be helpful. Be careful using too much perlite, as it is very light and will blow away easily on a windy day. Also, when you sift it or even shake the bag up too much, its good to use a mask, bandana, scarf or something else to breath through because there will be a whole lot of wee little particles floating around for a long time and you will be caughing them up or blowing them out your nose for a long time to come if you arent careful (learned that one the hard way). A lot of people prefer vermiculite because it looks better than perlite, but when you sift a bag, its common to lose atleast 25% because it tends to be much smaller. I'm personally a fan of fired clay, but that can be harder to find, and to actually buy a fired clay bonsai medium can be very very expensive if you can find it at all. There is no one mix that will be perfect for everyone and every tree, so you might have to play around a little to see what works for you, but 75:25 is a good place to start.
Be gentle when you change the soil, but don't be afraid. The best teacher is experience, and these trees can be a lot stronger than we give them credit for.