I recommend Bayyinah.com for Quranic arabic lessons by Nouman Ali Khan. He has many Quranic tafsir and Quranic arabic programs on his site including Arabic with Husna where he teaches his daughter easy 10-minute daily lessons on Quranic arabic. He teaches his daughter how to translate the Quran and discover meaning without the use of english translations. Through the 15 unit video series, he teaches beginner level arabic to advanced grammar nuances found in the Quran. He primarily focuses on Arabic grammar of the Quran much similar to the content of the Madina books. However, his teaching method and course structure is easier to follow. I used this website for 2 years and has greatly improved my understanding of the arabic of the Quran because he always uses direct examples from the Quran. Also, his sarf video drills helped strengthen my memory of verbal conjugation unlike any other source. The site require subscription of $11 a month but there is free 1 month trial
The popular Madina books are all available online as free PDFs which cover Quranic arabic but require you to read and do drills and practices on your own. There are video lessons for the Madina books available on youtube and other sites for free. These are the books primarily taught in masjids and Islamic schools.
There is also the use of the al Kitab books which I went through in college in the span of 6 semesters. The course includes online drills and videos along with in class activities. The books are designed for western students completely unfamiliar with Arabic. Ali Baa begins with the Arabic letters and how to read and write them. The 3 books teach MSA (formal Arabic) and Masri (Egyptian Arabic) and Shami dialects along with providing a broad exposure to Arab culture and history. The books come with CDs to learn on your own but the course structure is primarily designed for classroom instruction.
For a good online Arabic language dictionary, try this site which also has a masri dictionary (Egyptian Arabic) http://www.lexilogos.com/english/arabic_dictionary.htm