It’s always depend of the language level because “ok” is never used in “correct” or writing form.
Speaking with a friend for a party “Is it ok if I bring my sister ?” will probably be “J’emmène ma soeur, ok ?” (forcing) or “C’est ok si j’amène ma soeur ?” (asking) or “Est-ce que je peux emmener ma soeur ?” (mail/sms).
But to a stranger in front of a supermarket, you will use “Est-ce que je peux me garer ici ?” or more directly, in a hurry “Je peux me garer ici ?”

“Est-ce que correct si…”, “Est-ce que d’accord si…” and “Est-ce que bien si…” are all wrong, it will probably be “Est-ce que c’est correct si…”, “Est-ce que c’est d’accord si…” and “Est-ce que c’est bien si…”.

As a complement to rangzen answer, I would also use

(Est-ce que) ça va si … ?

(Est-ce que) ça dérange si … ?

(Est-ce que) ça pose un problème si … ?

From my point of view, Est-ce que je peux… and (Est-ce que) C’est bien si… are two good ways to ask what you want to ask. In the question about parking you can say Je peux garer ici? or Je peux me garer ici?. The same goes with bringing your sister.

I wouldn’t care too much about the nuance differences between the two languages. The French people know what you mean in both cases.

First let’s rule out “Est-ce que correct si…“, which is obviously… not correct. 🙂

“Est-ce que je peux…” is the natural way of asking, and the one I would usually use as a native speaker. The use of “pouvoir” really means we are asking for permission here.

Is it ok if I smoke here?

Est-ce que je peux fumer ici ?

As you said though, the meaning might be a bit different: you could argue it is a neutral way of asking. If you want to insist on your concern for others, you could use the verbs “déranger” or “gêner”.

Is it ok if I smoke here?

Est-ce que ça gêne si je fume ici ?

Est-ce que ça dérange si je fume ici ?

Est-ce que ça te dérange si je fume ici ?

If you are rather asking about rules you could use “Est-ce qu’on a le droit de +infinitif“ or “Est-ce qu’il est permis de +infinitif“.

Is it ok if I smoke here?

Est-ce qu’on a le droit de fumer ici ?

Est-ce qu’il est permis de fumer ici ? (formal)

“Est-ce que d’accord si…“ is not correct, but you were close. You could ask “Est-ce que c’est d’accord pour que +subjonctif“ or “Est-ce que tu es d’accord pour que +subjonctif“.

Is it ok if I go to the party tomorrow?

Est-ce que c’est d’accord pour que j’aille à la soirée demain ?

Est-ce que tu es d’accord pour que j’aille à la soirée demain ?

Note that I used a different example as “Est-ce que c’est d’accord pour que je fume?” would sound strange, although not impossible: it would mean “Is it cool if I smoke?”.

You can also use “Est-ce que ça pose problème si +indicatif“, which comes neutral if it is about smoking, but much more subtle for more sensitive topics.

Is it ok if my ex comes?

Est-ce que ça pose problème si mon ex vient ?

At last, rangzen gave an example literally translating into “Est-ce que c’est ok si…”, which works, but note that it is extremely casual, much more than the English counterpart.

I would recommend using “Est-ce correct si…”.