potere, riuscire and essere capace...

Recently I discovered I've been overusing the verb Potere and I've now been introduced to the words Riuscire and Capace. I'd like to understand the different situations in which I'd use these three words:

Here's what I think is true:

I would use Potere when discussing something I need permission for?

Also use Potere when there is some constraint, or something

Non posso uscire a presto stasera. (I can't go out early tonight)
Puoi mi portarmi un'altra carta? (would you bring me another card?)

Riuscire:

to succeed, to manage, can, to be able
to come out, to turn out, to come off, to be successful, to succeed
non riuscire - to fail

I would use Riuscire when discussing something I can or cannot do-- in terms of ability...
Non riesci giocare calcio con un braccio rotto. (You can't play soccer with a broken arm)

You can not play anyway! Not the best example ????. this is better:

Non riesco a colpire il bersaglio (I fail to hit the target ... I could but I'not not good with gun, bow..etc)

Riescono a nuotare adesso perché hanno preso prendono dieci lezioni.(They can swim now because they took ten lessons)

Essere Capace di:
I would use as an adjective when describing ability or capacity to do something?
Sono capaci Di lavorare qui (They can work here)
Non sono capace a di parlare francese. 

Non so parlare francese (I can't speak French)

Which word would I use when saying:
I can't eat cereal because I am allergic to gluten *would this be like I'm not permitted to, or I physically am not

Non posso mangiare cereali perché sono allergico al glutine

I can't buy you that dress *does the word choice change depending on my reason? ie. if I can't buy it because I don't have money vs. I can't buy it because it's too short and it would be more of a permission thing?*

Non sono capace di comprare quel vestito (non ho abilità per farlo, in ex blocco psicologico, oppure it is online and I'M not god with computer... because I lack of some skill...)

non posso comprare quel vestito (qualsiasi motivo ..any reason .. Ok anyway)

non riesco a comprare quel vestito (not enought money or time or for my lack of ski 

I would appreciate corrections in my sentences and also in my understanding of these three words and the situations in which I'd use them? Other examples are welcome.

Grazie per tutto!

you're welcome