Sorry if I wasn't clear. I want to know how to say "I just [did something]" in Tunisian Arabic. As in:
     • He just ate.
     • I just arrive.

So the equivalent of لسه in Egyptian Arabic (لسه وصلت، إلخ). I was told that it's مازال كي (like مازلت كي وصلت), but I'm not able to find a lot of examples of that construction, so I'm looking for additional information.

Now, as other people mentioned, which variety you decide to study (first) will depend on what your goals are with the language. If your goal is to be able to watch the news and read literature, then by all means study Standard Arabic. If your goals involve travel and interacting with people, though, I would recommend that you learn a dialect first, then Standard Arabic afterwards. (Most native speakers would advise the opposite.)

If someone was going to learn just one variety of Arabic, I would recommend Egyptian, for a few reasons:
     • Egypt is a great place to visit, and obviously Egyptian Arabic is the best way to get around — Egyptians in general don't understand dialects other than their own. (They don't have to, because everyone understands them; they're a bit like English-speakers in that way.)
     • If you travel somewhere else, almost all Arabs understand Egyptian, and a lot can even speak it
     • There are a ton of movies and songs in Egyptian Arabic, so there's lots of fun things to do
     • A lot of American movies/ TV shows are dubbed into Egyptian, including children's programming (most Disney movies are dubbed in Egyptian, aside from a couple in SA). These are incredibly useful resources for learners.

Now, I think people should still learn SA, once they've got a solid hold on a dialect. As far as ease of learning, the order doesn't really matter: learning dialect will make SA easier; learning SA first will make learning dialect easier. But you'll end up with more native language-switching patterns if you do dialect first. (I wish I had.)

Even if you want to focus on North Africa, you'll probably still need to learn an Eastern dialect, because Easterners don't understand the NA dialects well. But this is not to discourage you — Tunisian Arabic is wonderful, and well worth the effort!

To answer a couple of your specific questions:

     • You're right that Standard Arabic (or SA) is not generally used as a spoken language. It's the language of school and mosque, some television programs (especially religious ones, news broadcasts, or programs for children), and almost all written materials. But it's no one's mother tongue: it hasn't been spoken as a native language for at least a thousand years. But it is the same in all Arab countries, and most people do understand it and could speak it if they had to. (But most are not comfortable speaking it for extended periods of time, unless they're very highly educated.)

     • The dialects are very different, both from SA and from each other. Learners of Arabic tend to consider them completely different languages (native Arabic speakers will strongly disagree with that). To give an example, I have a pretty high proficiency in Tunisian Arabic, and because of this I can understand Libyan Arabic pretty well. But I can't understand Algerian Arabic well, and I can't understand Moroccan Arabic at all. And if I speak to an Egyptian or a Syrian using Tunisian Arabic, they can't understand me at all. There's just huge differences in the sounds, vocabulary, and grammar.

     • Tunisians (and other North Africans) do use quite a bit of French. There's a good number of French borrowing into the dialect (though not as much as people think), and they'll code switch into French when they're discussing higher-level topics. But if you go there to work on your Arabic, do not tell them you speak French. They won't speak to you in Arabic if you do. Nothing intentional, they're just really used to speaking to foreigners in French, and it's weird for them to meet a foreigner who speaks Arabic.

Yes, Arabic is difficult. Very, very difficult. The main reason it's so difficult is because of the many varieties: you don't learn "Arabic", you have to learn at least two "Arabics" to be able to really use the language (Standard Arabic, and at least one well-known dialect, like Egyptian or Levantine. I very much disagree with people who said you could get by with just MSA: even if people could understand you (most will), and even if they could respond to you in MSA (not guaranteed), they definitely wouldn't be comfortable maintaining a long conversation in MSA, and you wouldn't be able to understand anything that was going on around you, when people weren't speaking directly to you. You need to learn both.

نعم، اللغة العربية صعبة جداً جداً. السبب الرائسي لصعوبها هي الأنواع المتعددة لها. ليس لديك أن تتعلم "العربية" ، أما لديك أن تتعلم إثنين "عربيات" على الأقل: العربية الفصحة وعامية من العاميات المعروفة، مثل المصر أو الشامي. لست متوفقة اطلاقاً مع الذي يقول إن العربية الفصحة تكفي. حتى لي فهموك الناس (أكثرهم ستفهمك لو تكلمت بالفصحى)،  وحتى لو استطعو أن يردوك بالفصحى (ممكن يستطيعون، لكن ممكن لا)، لم يشعروا بالراحة، وأنت لم تستطع تفهم أي شيء يحدث حولك. لذلك، مفروض على الطالب الأجنبية أن يتعلم العامية والفصحة الإثنين.