Ichimoku is a complex indicator especially because it also plots into the future rather than present. Maybe we will support it in future (if there is enough requests for it) but I don't see a plan for it at least in near future. Sorry, but this is what we think as of now.
I Edgar, If I test it now it is showing me updated data. Many times it happens that data by providers (like Yahoo, Alphavantage, etc.) aren't updated and so Stockalyze shows old data. When you see this problem I will advise to check the data in Yahoo!, if it is updated there then only it is Stockalyze that failed to update it. I think it will not be the case but if you see this then please inform us.
You can test for stocks from more than 40 countries and US and Brazil are also included.
Stockalyze has built-in Trading System that uses RSI(14). If you want to use RSI(2) then you will have to create your own Trading System in Stockalyze which is very easy and you can do that without use of formula or learning to program. Have a look at help page here to know how you can define your own Trading System. You can also watch demo video and see how to do it.
In Lite Mode you can define your Trading Systems but will not be able to save it and so you cannot use it. But you can definitely get first hand experience about how to define your own Trading Systems.
The answers to all your questions is "yes". And you can even try most of what you asked here in the Lite Mode (free version) itself and then make up your mind if you need to buy Pro Mode license. Stockalyze supports exchanges from as many as 40 countries and so it is usable from across the world. Again you can just give it a try and see if it has supports of the exchange you are interested in.
[I was on a long vacation and so the delay response]
Backtesting in Stockalyze is about testing stocks individually and not about portfolio as a whole and so it always assumes you are investing entire amount into single stock and then it gives you result about how good or bad the trading results would have been. With this setup I don't think position size or position value is required. Please let me know if I have explained it. In case there is something that I am missing then please let me know.
[I was on a long vacation and so there is so much delay in my response.]
It depends on what you want to do. As of now there is no way to define indicators using formula. But if you want to create indicators that uses other indicators then you can do that. And that is available in Lite Mode too. You can see indicator of indicator and composite indicator video to know how to create new indicators using existing ones. May be this is what you need. Please let me know if it doesn't fulfill your requirements.
[I was on a long vacation and so there is considerable delay in my response].
I think what you are asking for is to place a "limit order" when sell condition triggers. A limit order with expiry will make it possible to achieve what you are asking for. Do you think I am right in understanding your suggestion? If so then I think it should be possible to do that in Stockalyze.