Remember that the word 'able' is an adjective.
The simplest way to translate the word 'able' into Italian is 'capace', or as Beatrice says, 'in grado'.
So 'Soon you'll be able to do it ' translates as 'Presto sarai capace di farlo'.
'I wasn't able to do it' is 'Non ero capace di farlo' and so on.
If you think of 'to be able to ' asthe translation of 'essere capace di ', you'll realise that you always need the verb 'to be' before it. That's why you can't say 'I able to' - 'able' is an adjective, so it needs to have a word like 'be' or 'am' or 'was' or 'are' before it.
As for the subjunctive - don't worry about it. There's no need to 'complicarti la vita', as you say! English does not have a form which is equivalent to the Italian congiuntivo. None of your statements beginning 'Che io riesca' and so on would be translated with a subjunctive form in English. English grammar is much simpler than Italian in this respect. We would just use an indicative form.
«Che io oggi non sia riuscito a parlare inglese in modo veloce, non ha importanza»
= It doesn't matter that I wasn't able to speak English quickly today.
I hope that I've been able to help you :)