"I can speak a little bit of Chinese."
"我会说中文一点儿“ sounds unnatural; I don't think it would mean the second part of your question, either; I think to say what you are asking you would say “我说一点儿中文”, and specify a time period, or maybe "我会说一点儿中文" (and also give a time period); ending the sentence with 一点儿 definitely sounds weird.
According to this article, https://www.writtenchinese.com/the-3-cans-whats-the-difference-between-hui-keyi-and-neng/
会 (huì) is used for a learned skill such as being able to ride a bike, swim or speak a foreign language.
可以 (kě yǐ) is used when expressing permission to do something.
In English, 可以 (kě yǐ) is probably better translated as ‘may’, although ‘can’ is obviously less formal and more commonly used in oral English.
That's a rather strong opinion denouncing the dialect of the capital. Undoubtedly you must be from a town that uses SAE (Standard American English) and sneer at anyone with an accent, or perhaps you believe that an American accent is the equivalent of 儿 化 音 and no one should be teaching English with an American accent, only British varietals. I'd prefer to learn the nuances. Isn't that why we're learning foreign tongues to begin with?
Please, stop using 儿话音，that is not mandarin! Beijing hua isn't standard putong hua, and it's horrible.... If you want to teach people proper Chinese, you need to stop this stupid 儿话。。and if I ever see 咱们 I might turn insane, only few people in Beijing talks like this and it just sounds horrible.
You're right that 北京話 is NOT standard 普通話. Putting 兒 at the end of so many different words in their dialect is not standard at all!!
一點兒 is one of the few standard 兒化 words though. I think it's fine if publishers using 兒化 teach using it, but often they don't make the point that it is very regional!!
And agree with you on the 咱們 and the horrible sound of 兒化 as well.