You should’t use an article in parler le français:

Est-ce que tu veux que je parle français ?

C’est difficile pour moi de parler français.

Otherwise, these two sentences are correct.

1. Their difference in structure is due to the fact que has to be followed by a conjugated verb (like "that" in "that I speak") while de must be followed by an infinitive (like "to" in "to speak").

2. The following sentence is incorrect:

Est-ce que tu veux moi de parler le français ?

A possible but a little far fetched sentence could be:

Est-ce que tu veux de moi que je choisisse de parler français ?

3. The next sentence is not idiomatic, difficile and que do not mix together here:

C’est difficile que je parle français.

The is no evidence yet it is ungrammatical though, but the fact is this combination sounds odd and essentially unused in written French or in standard spoken French.

There are however similar constructions that are definitely grammatical:

C’est bien que je parle français.

C’est ennuyeux que je parle français.

and even:

Il est bien difficile que vous vous trompiez. (Tocqueville, 1858)

To answer 1., it doesn’t make much sense to consider "me to speak French", because the me can come from very different constructions.

You want me to [verb] = Tu veux que je [verbe]

It is hard for me to [verb] = C’est difficile pour moi de [verbe]

The two constructions aren’t even close in English, and you should consider them as a whole and not chop parts of them who look alike and assume they behave the same way.

2. No, vouloir in French is always like you’re taught. There is no way to make it look like the English "I want you to …", it’s always "Je veux que tu …"

3. No, but in books it would be correct to say :

Il m’est difficile de parler Français

Just know that it exists, to satisfy your curiosity, but don’t use it in conversations, it’s way too formal.

• Me voudriez-vous que je parle en français/ que je parle du français ====> would you like me to speak in French/ to speak French.

• me voulez vous que je parle en/ du français ====> do you want me to speak in/.0.. French.