刚检查出什么病means that Xiaoli's father has just been examined that he is sick,as for what illness he gets,this sentence doesn't tell us. In this stence,可is a word to express an emotion which shows that the speaker appreciates the apple very much because there is no such kinnd of apple in the speaker's hometown. 顺便means while a person doing sth which is his main task,he also does sth else,but this ofen happens in a convenient situation.

1. 小李的父亲是今年三月住院的，刚检查出是什么病。 This sentence means xiaoli's father was sick, he have went to hospital in March this year, but still now he just cheaked out what is the disease. 2. 这些苹果是小张的父亲从家乡带来的，咱们这儿可没有这么好吃的苹果。 Those apples were been brought by xiaozhang's father from his hometown, we don't have such delicious apple! 可in this sentence ues for stress the speaker's viewpoint "we don't have!" and "the apples are delicious!" 3. 是来看儿子的，顺便也买点儿书回去。 He/She came to see his/her son, by the way he/she bought some books. the phrase 顺便 in this sentence used for illustrate that his/her main propose is to saw his/her son, brought books was just by the way. Do I explain clear? Maybe many mistikes in my english, but hope I explained well.

1.What does mean 刚检查出是什么病。 this sentence In English? 小李的父亲是今年三月住院的，刚检查出是什么病。 Li's father was in the hospital in March, but just examine what kind of disease recently. 刚=just recently 查出＝examine 是什么=what ( kind of) 病＝if serious healthy problem＝疾病 = disease( eg:cancer ) ＝if common healthy problem = sick ( eg:vomit, cold, fever) 2.what does mean 可this sentence In English? 咱们这儿 可 没有这么好吃的苹果 Our here really haven't tasty apple. [this word usually uses in spoken conversation.] in this case, 可chould no be explained as [ can可以 ], It can explain as [ so/really... ] in short, it is a modal adverb in this sentence for increase the emotional expression. eg:我哥哥可聪明呢！ My brother is so intelligent. 你像猪吗？ are you look like a pig? 可不是呢！Absolutely NOT!!! 3.What does mean 顺便 this sentence In English? 是来看儿子的，顺便也买点儿书回去。 I'm here for look up my son, also buy some books back on the way. 顺便= do something [conveniently] / [while] I'm/you're at somewhere / might as well eg:While you are fixing the car, you can give it a wash. (当)你在修理车时候，可以顺便洗一下它。 For now, It's is quite hard for me to translate those words, as I'm a beginner in English, I hope I could help you. 作为一个英语初学者来说，翻译和解释对我来说有点难度，如有出错，还望赐教。

1.小李的父亲是今年三月住院的，刚检查出是什么病。 Xiao Li's father was hospitalized in March this year, just check out what is the disease. 2.这些苹果是小张的父亲从家乡带来的，咱们这儿可没有这么好吃的苹果。 These apples are Zhang's father brought from his hometown, we can not have such delicious apple. 3.(我)是来看儿子的，顺便也买点儿书回去。 I came to visit my son, and to buy some books by way .