How are cells able to act and react to their surroundings?
They have sensors both facing the outside and their inside called receptors which detect a whole bunch of things, from changes in electrical charge to nutrient levels to hormones. These receptors create signals in the cell. The exact type of signal depends on the receptor. Often it has something to do with turning on or off one or several genes.
how can cells form more different cells at the right time This maturation process requires a sequence of signals, sometimes from outside, sometimes from within and sometimes both. A stem cell will divide and the daughter cell will react to certain signals to make the first step in the development, which results in turning on one or more genes. These genes are regulatory genes which in turn only turn on or off other sets of genes which in turn... you get the point, it's a network of things that regulate each other. That these steps are taken can be dependent on outside signals, like hormones or on inside signals, like "self-test" signals that show if something went wrong so far.
How does a cell know that is has to become a bone-cell When a new animal is formed, starting from the zygote (egg+sperm), the development is regualed by maternal signals. It starts with signals that give the developing embryo directions up/down - front/rear - left/right. Once that is done a fairly rigid program is started where again networks of genes regulate each other to make cell divide exactly when the should. In a developed animal or human there are no more stem cells that can do everything, only specialized stem cells (they are pluripotent and not totipotent, to use the fancy words). Those specialized stem cells are for examle in your bone marrow to make blood cells and in your skin to regnerate your skin. The decision between different types of cells are regulated as I have described above.
at the right place Those receptors can also detect direct cell contact, which enables a kind of communication with the direct neighbors. So a cell "knows" that it is surround by, say, one type of skin cell. But these signals can also be transported over distances. Here the signal intensity is used to create a kind of web of coordinates. Imagine a complicated a game of battleships: the cell gets one signal that is 6 strong and a different signal that is 4 strong (those numbers are completely made up by me just to give an idea about strength). So this cell is closer to the source of the first signal than to the second. Combine 10 or 20 of those signals and you can estimate your position in an organ. Take this together with your direct neighbor and cells "know" where they are.
This whole topic is very interesting but also very complicated. It takes literally years of cell biology lectures to get a grip on this and my answer is vastly (over-)simplified. If you need more info, just ask.