To sum up, what Tudousi~ said above is basically correct, but there are still some points you need to pay attention to. a)This sentence is not totally correct. There should be no "bìng", and the correct tone of "xue" should be "xué". If you insist on adding conjuncions between these two sentences, you can say "Wǒ shì yīng guó rén,bìng qiě/ér qiě wǒ shì xué sheng", but in fact, whether in speaking or writing, there is no need to use such conjunctions as "bìng qiě" or "ér qiě" here, because they only make the sentence awkward. b) I believe we native speakers would say "Wǒ shì gè yīng guó xué sheng",which means I'm a British student, in a shorter way. However, you can also say "Wǒ shì yīng guó rén, shì gè xué sheng", if you want to stress that you're a student. Using "gè" here is to make this sentence more idiomatic, for this type of words typically smacks of Chinese language. Sorry that it's too complicated to explain away its uses here.

bìng should be deleted. You can speak in 2 sentences. Wǒ shì yīng guó rén. wǒ shì xuè sheng. 我是英国人。我是学生。 shorter expression: I am an English student. Wǒ shì yīng guó xuè sheng. 我是英国学生。

1) This sentence is right in grammer.However,"bìng" can be left out.Because in my opinion,when use"and" connect two sentences in English,it is not so necessary to translate it into Chinese.I think "Wǒ shì yīng guó rén,wǒ shì xuè→xué sheng."is better.If you really would like to translate"and"between two sentences,"bìng qǐe","ér qǐe"are used in this situation,which means you can say "Wǒ shì yīng guó rén,bìng qǐe/ér qǐe wǒ shì xué sheng" 2)A shorter way to say this is "Wǒ shì yīng guó xué sheng". I am not so confident with my English as much as my Chinese.But really hope you can understand what I try to explain.

我是英國人並且我是一位學生. Basically, many translator don't translate a foreign language into another language directly because sound bizarre but they will help you to think a better and smooth sentence to replace which means it could be more approachable to your culture in usage. Such as food. Chinese food is different from your food and we only can use Chinese name directly to say it in English sounds for your understanding or indirect ways to find your similar English food to represent our Taiwanese food or Chinese further towards better to realise our similar ingredients. la ~~ Hopefully, you understand my explanation very well.

there's no "and" between verbs in Chinese thus _the_sentence_ isn't right but it consists of two correct parts and the word "student" is with 2nd tone, /, not with 4th, \ i'd write it as: "Wǒ shì Yīng-guó-rén. Wǒ shì xué-sheng"