To reckon ( there is only one way to spell it) is not slang. It means to calculate or to estimate. You can think with your brain, but you can reckon with you brain, or a calculator, or a pen and paper. This means that yes, you can use reckon in most cases where you might say think. Side note: to those giving out advice in these forums, if it's a word you don't use, then consult a dictionary before telling someone else your wrong opinion.

In British English, 'reckon' and 'think' are both used to express opinions but 'think' is part of the standard language and is used universally and in all situations. 'Reckon' is much more colloquial. It's only used in speech and very informal writing and not by everyone. 'Reckon' is also used more to introduce a guess or supposition rather than an idea based on evidence. As for the difference between the questions, I'd say that they can all express surprise, scepticism, or the idea that what you just said is obvious. However, only "Really?" would be used to express polite interest. 'Reckon' also means to count or calculate. The expression, 'by my reckoning' is common and means 'according to my calculations'.

Good answer from Ian. I live in a part of the US where this term is used (Texas -- a place traditionally associated with cowboys, as Hyudoro says), but I've never used it myself. In the US, "I reckon" is mostly only used by people with strong southwestern accents.

Recon (or recken, or reckon) is slang. It means the same thing as "to think", but only certain types of people use it. You don't need to use this word, but it is good if you understand it when someone else says it. One strange thing about it is that it is a shared slang term by some Australians and Americans. But I never use it. Я являюсь носителем английского языка, но это слово прозвучало бы странно, если бы я использовал его.

Reckon and Think have mostly the same meaning, but Reckon is more colloquial and has a "southern" or "cowboy" feel to it.