Both of your sentences in (1) are incorrect. They should be:
a. There are some ways of writing [the sentence continues].
b. There are some ways to write [the sentence continues].
The plural ways is important. Now that that is out of the way...
Your examples in (1) are not quite interchangeable. In mathematical terms, you might say that they are equal, but not congruent (or congruent, but not identical). The nuance is difficult to see in that pair of examples, but I'll try to highlight it as best I can.
In 1a, ways of writing is a noun phrase, and can be replaced with a single word or a different phrase without changing the underlying semantic structure of the sentence.
In 1b, though, ways stands alone as a noun and to write is the predicate of a separate clause.
The difference is subtle, I will grant, but it is a difference. Ways to write could not, for instance, be directly replaced with the noun orthographies or the noun phrase writing systems easily, although one can imagine them easily replacing ways of writing in any number of contexts.