I guess it depends on what area of maths you are speaking about. In group theory and most of the algebra I have encountered for example it is customary not to write the product sign it in most of the literature I have checked, maybe in other ones people write it.
And I have NEVER seen a case where YX stood for Y+X, even for abelian groups, where the + sign is used, it is written Y+X (and YX when using the multiplicative notation), it almost always is product or composition of functions.
If you are working with numbers, though, it is more used, to avoid confusion, but whenever it is clear, it is omitted.
x is not used often for multiplication because it usually denotes direct products, which can cause confusion, so * is the usual chosen symbolif there is one.
It depends on the context, and some people may want to use a convention or other, at the end of the day all it matters is that you are consistent and clear with what you mean.
And yeah, LaTeX takes a bit to get into, but afterwards it is such an amazing tool when writing any maths. If you do not use it, I highly recommend it.