What role would you say does the community of believers play in one's own spirituality?
I say this with no intention to offend anybody, but for me, the "community of believers" is just necesary when you believe in something you also doubt; so you need others to reinforce this. Actually belief and doubt cannot be separated easily, and with blind belief always comes the shadow of doubt.
The Buddha said that admirable friendship in the holy life is the whole of the holy life.
Jesus also stressed the importance of associating with the like-minded, in his name.
The commune is another matter, communes form when people want to live a spiritual life together, no need for belief or dogma. Everyone can follow his/her own heart. Most communes revolve around a spiritual guide; this only works if the spiritual guide has reached the realization himself (which is usually not the case). But there are also communes without a specific leader (although they read scriptures, they don't consider them "law" but just aids in the path).
A religious dogma congregation is different, they are just needed to cheer and reinforce blind belief.
When Jesus says "Gather in my name", he doesn't mean to praise him. But to gather for the goal of achieving Christ-Consciousness in this life; not in a place after death that you have to blindly believe in.
Would you say that spirituality is primarily a solitary endeavor of studying various texts and applying some tenets from them to one's daily life?
Not really, it is a solitary endeavor alright; but does not necesarily include the study of scriptures. What is really necesary is to know oneself; scriptures can help and are a very good starting point, but getting to know oneself is indeed a solitary endeavor. Faith in the sages who have achieved have proven to be a good inspiration to continue in this solitary path.
If you meditate, then you will be totally alone, even if you have people meditating around you (which actually helps), you are alone with your thoughts. And you don't need a group of people to encourage you or cheer you up, 'cause getting to know yourself is a goal into itself.
We are bound by our "incomplete past actions" or karma, or repressions; you may call it different ways, but these control most of your thoughts and therefore present actions. If you enter into this realm, you will start seing the causes of the thoughts (where they originated from) and just by seing you will be free of them. Nobody can do this for you, psycoanalisys can help, but it won't get you to the end of the road.
Without taking part in an organized religious community, how can one have hope that one will atain what the various texts that one reads are promising?
There is a Zen saying: "When the disciple is ready, the master arrives".
The work you do on yourself can only get you so far most of the times. You will see the results of your practice without the need of external guidance.
But if you reach a point where you feel that you are stuck, then a proper guide is needed.
Very few times a man reaches to the realization all by himself, most of the times a master is needed. Even Jesus had a master who guided him at the beggining of his journey (John the Baptist).