Some languages have multiple expressions to identify, address, comprehend, and interpret a single concept and/or experience.
Are limits placed on understanding and describing aspects of cognition due to the finite lexicon being used to explain a mental concept or experience?
Does language create a bottleneck situation where the available lexicon used to define certain aspects of cognition and its experiences are inadequate for understanding the true definition of that experience?
This is a hot topic of debate, so my answer will be an incomplete one.
There are actually two separate questions here. One is on language and the other one is on environment.
My answer is no; different languages do not limit the conceptual repository of human mind. The current ongoing debate is partially on the Pirahã language. Everett studied this language and after seeing that it does not have syntactic recursion, he claimed that it demonstrates that Pirahã community somehow could not think recursively. Of course this is a very simplified view and may be a little misinterpreted and/or a provocative understanding of the Sapir-Whorf hypothesis. But I believe that the main problem is on the theoretical grounds of grammar. Steedman's CCG shows a very powerful alternative way of looking to grammars. It is computational and combinatorial. I don't know any particular studies on Pirahã with combinatorial grammars, but that would be an interesting issue to investigate. My personal opinion is that this thinking of "language effects the way of thinking" is also a bit dangerous and open to manipulations too much.
Environment definitely affects the cognitive abilities. There are several studies on this. You can search the internet for papers such as Gathercole (1999) or Gleitman, Elissa, Newport (1995). These are the ones that came to my mind immediately. One of the facts is that late exposure to language entirely limits the grammatical abilities. Environmental feedback is also essential. It may be hard to observe physically impaired children but there are also studies that focus on deaf children in hearing families in the absence of sign language. These are interesting studies, but the bottom line is: yes, environment affects cognitive abilities.
I'm not sure what you mean by cognitive capacity, but I absolutely believe that language shapes the way we think. The collective nouns, verbs, and phrases of a language are the categories by which a culture interprets things.
Consider seizures. Our culture may call them seizures, and a doctor might posit that their cause is epilepsy (or something). That's how we would approach understanding the phenomena. In another culture, they could say that the person is possessed, and they might posit that they cause was an evil spirit. That's their understanding of the phenomena. It might be easy to dismiss that, but if you think about it you'll see that most of us only understand epilepsy as much as they might understand how the spirits work. It's just a word used to explain something. Even the word epilepsy itself, actually means to be taken upon and seized. In it's original usage it was implied that some otherworldly force was doing the seizing. Can you imagine if the other culture I invented had created modern science? Surely their terminology would revolve around the term for "seized by an evil spirit".
Or consider something as basic as color perception. To us, it feels absolute and more an attribute of external reality than anything internal. But even how we understand color is variable with language. Heinrich (1972) looked at the Eakimo and found that the way they categorize color was significantly different from ours, and follow language lines.
Another reason why I think that yes, language defines understanding, is seen in modern science. Modern science is almost defined by the rapid and dizzying creation of new language. As we build a finer grained understanding of things, new terms need to be created to even understand the topic, let alone discuss it. Consider Organic chemistry, where a virtual new language has even been created to describe molecules.
The last point I have to make is that there is always another distinction to be made. We haven't gotten to the bottom of anything yet, and I don't suspect we will for a long time if ever. Our words are categories, which means they contain multiple things that are similar to some degree. House is a broad word, a large category. Mansion, hovel, etc... are more narrow words, less inclusive categories. And so on. How fine a category could we make to describe homes? Theoretically we could have a word that perfectly describes each individual house.
The words available to us define how we can think of and communicate things. Different cultures have different words available to them, and thus think of things differently. I had a very interesting conversation with a Catalan friend about words in that language that have no correlate in English. it was very enlightening.
References
http://www.npr.org/2011/09/30/140954025/science-diction-the-origin-of-the-word-epilepsy
