Great, " First of all" is a right form but "to begin with" too. I learnt it by the reading of " A Christmas Carol" by Charles Dickens. It begin with this expressioni : " Jacob Marley was dead: to begin with."
Yes, you're right: ing form is better than simple present which however isn't a mistake.
I prefer "is speaking it" because when the italian traslantion is " il + verbo" " il parlarlo" in this case, in my opinion the ing form is preferable (better).
Yes, it's another right form to express the concept.
Yes, you're right. I have to put "by".
You can omit "that", but if you put it, it isn't a mistake.
All right, but keep in mind that Dickens wrote "A Christmas Carol" in 1843 and some if his sentences are not exactly up to date, just as Manzoni's "Promessi Sposi" are not a proper reference of Italian modern language.
As I said before some forms can't be considered grammar mistakes but they just sounded like a literal translation from Italian.
The 'speaking it' case looks better only as an 'Italian literal translation' but in English is a lot more common to hear and read two simple presents in that sentence.