This is a big question: you need to be clear about a few things before we look at the examples. Best make yourself a cup of coffee before you start reading :-).
"Suggest" and "say" are both normal verbs: they both take a subject, they both take an object. The object is what you are suggesting or saying. There are lots of possibilities for things that you can suggest: see here.
One of the ways to specify a suggestion is with a that-clause:
I suggested [that we should update the web site]
This is where it gets confusing: sometimes we leave out the "that":
I suggested [we should update the web site]
If you want to specify a recipient- the person who receives what you are suggesting or saying- you have to use the preposition "to" followed by the a noun or pronoun.
If the suggestion is a noun, it goes next to the verb, with the recipient at the end:
I suggested refinancing to John
If it's more complex we put the recipient first, followed by the object.
I suggested to John [that we should update the web site]
Sometimes the 'to' is omitted: the noun or pronoun on its own is called an indirect object. The indirect object has to go between the verb and the object: here are examples with and without the 'to'.
I gave the file to John - normal
I gave John the file - indirect object
Taking your examples one at a time:
I suggest you to pay the tax
This is indeed wrong: "to pay the tax" isn't one of the allowed objects for "suggest". If you used "advise" instead, that works, because advise takes the recipient as an object:
I advise you to pay the tax.
I suggest you pay the tax
This is correct: if we put back in the "that", we get
I suggest that you pay the tax
I said something to her
This is correct: we have object-to-recipient
I said to her something
This is wrong, because a simple noun object must come first unless it's an indirect object. If you were to replace "something: with a more complex expression, the word order would be correct:
I said to her that she should just forget him.
I said to her "Just forget him!"
The indirect objects link contains a list of other words that work like this.