As a point for you as a new player, I wouldn't recommend Japan as a first campaign. Learn with a nation like Argentina or Brazil, where you won't be the center of attention, and you can learn each part of the game in small increments. Then go for the USA, just so that you feel powerful and learn what conquering the world is like without any real fear of losing. Then something like Japan or Germany, where you do have to work for your victories. Then you can try something sadistic like Communist China

(only campaign I ever straight up lost was as them) Just some advice.
What about infrastructure in the most factory rich provinces?
Does that actually do anything past 100%? To my knowledge all of Japan is at 100%. Anyway I still don't think infrastructure is a good investment. Keep in mind I'm not using CORE, just vanilla AoD with a few event mods.
should I put the slider to the rightmost position for those two resources or what?
No, because I think that's telling the AI how much you want. I put oil in the middle and rares at about 1/4 over. It got me enough.
Yes, and it will net you a 15 IC increase by 1940. Building factories are in general a contested thing to do among players. I wouldn't be surprised if someone else came into this thread and told me I was wrong. As countries like Germany and the US, probably it is useless. But as Japan, you're not in a war that you can lose until 1942 anyway, and you're basically not expanding your navy at the expense of factories, so that you can build more later and get more tech slots.
How much money do you spend for research teams
As much as it takes to have all the slots filled. Japan only starts out with five slots, and it needs to do more research. Prioritize machine tools, aircraft carriers, and tac bombers.
Speaking of tac bombers:
Try and build a few more. You might not be able to because you have no spare production, but try, maybe in 1938 or so. They help in China a lot, keeping the Chinese org low. Use interdiction. Use the ones that you do have at the beginning of the game constantly. It will build up the experience of your bomber commanders a lot, helpful when you start fighting the USA.
Is it worth for Japan to research techs in advance?
Never, except for improved machine tools, which you should start right after you finish basic machine tools. Kawasaki Heavy Industry is a great tech team. Nothing else is worth the incredibly slow speed of research, and there is always something else you can do in the mean time. Capital ship tech perhaps in the six months before its historic year, but only if you can start a production run right after you finish the research.
I shall make one serial of infantry
You misunderstand me. A corp is three units. You should start three units of infantry, with one each of those brigades. Make them indefinitely. The gearing bonus will eventually get so high that you'll make a new corp every six weeks or less. Don't stop until you're sure that you'll be able to beat the Chinese. Then switch over to marines. Also have a production run of garrison with MP brigade, to help control China. You'll probably still get a few revolts, but they'll help.
What are armored car brigades good for?
They're relatively cheap and they give you another edge in quality over the Chinese. These units are designed to be grouped into corps of three, led by Lt. Generals. The three different brigades complement each other. I would say just get another unit of artillery, but they're expensive in AoD, and ACs are cheap. So one of artillery.
Should I start building those few capital ships from the beginning of the game?
No. Keep your lone carrier serial going, upgrading it as you increase your tech. I'd start building in 1938-39, which is still in time for the war with the US.
Also, I made a mistake when I wrote my first post. I was playing a Fascist US campaign, and I forgot about the navy in San Diego

, which made me think that they had gimped the USN in AoD. Turns out I was wrong, and the US battleship fleet does still exist. So the USN is better than the IPN, so you do need to build quite a bit. Of course, war with the US avoidable, and not declaring war screws up the ai in all sorts of fun ways, or declaring in 1943. That peacetime penalty to the US is quite large.
As for navies, I'd recommend reading this article:
http://www.paradoxian.org/hoi2wiki/index.php/Naval_Primer
True it's HoI2, but the basic principals remain the same. I don't think AoD has a wiki, but many things are basically the same anyway, and if they're not they're usually simpler.
All of them but the garrisons. Have a force in north China, and keep a force in reserve in Japan or Taiwan, to invade Shanghai and advance to Nanking and beyond. Make sure you have HQs in both forces, one should be enough for Shanghai. Don't lose them (it's really hard to lose land units short of being encircled anyway), because you won't be able to build more.
I never support the coup. It isn't worth the dissent hit, and the loss of relations.
Don't know about the convoy thing. Weird, just go under trade, go to convoys, and tell it to automate everything. Saves you major headaches (except when it refuses to send escorts when the convoy is going into a warzone).
I'll have anything else to ask I will do so when the question pops out during my gameplay.
Feel free. Though perhaps this should be moved from the AAR forum.