Is the second part of this sentence grammatically correct?

Solution 1:

You need parallelism (not always an essential, but certainly in this case) in the sentence:

• It is well known that social media platforms can make it easier to communicate with others and that this form of communication is fast and convenient.

=

• It is well known [that social media platforms can make it easier to communicate with others] and [that this form of communication is fast and convenient].

or

• It is a well known fact that social media platforms can make it easier to communicate with others; it is equally well known that this form of communication is fast and convenient.

.....................

None of

• It is a well known fact that social media platforms can make it (a) easier to communicate with others and (b) how fast and convenient this communication is.
• It is a well known fact that (a) social media platforms can make it easier to communicate with others and (b) how fast and convenient this communication is.
• It is (a) a well known fact that social media platforms can make it easier to communicate with others and (b) how fast and convenient this communication is.

work. I can't find a deleted form that does work, and would say that for this reason, the original is ungrammatical.

Solution 2:

It doesn't work at all. If you are going to say "It's a well known fact that 《something》and 《something else》" then, if it's going to be grammatical and make sense then "It's a well known fact that 《something else》 " needs to be a proper sentence.

The reason for this is that the word 'and' links 《something else》back to the start of the sentence. In this case removing the first fact and the word 'and' gives "It's a well known fact that how fast and convenient this communication is" which is almost nonsense. The writer needed to express the concept of speed and convenience as a statement of fact, which is what you have done in your version 2. You could also have said "...and that this communication is fast and convenient".