Hi, it seems that it’s kind of difficult to express the most simple word in Chinese… haha
As for me, “and” could be used in the below situations, for your reference.
Firstly, let’s talk about your examples.
1 I don’t you have to translate “and ” into something, so you could not translate “and ”here. The meaning of this sentence won’t change.
“Senior student in university” could be 高年级学生, also is “大四学生” （there are four grades in university, 大一 freshman, 大二 sophomore, 大三 junior, 大四 senior）
I am a senior university student AND I am 21 years old.我现在是高年级学生和我二十一岁。
我是一名大四学生，我二十一岁了,Or you could combine this two meaning together, which would be ”我是一名二十一岁的大四学生”.
2 Both.. and..=（既）…也…，it will be ok if you don’t translate 既.
I want to both study AND travel.我想学，也想旅行。=我既想学习，也想旅行。
“and” could translate into 和, 然后, or just a comma”,”
1 Mary and Jenny attended their friends wedding party together yesterday.
The structure of : A and B = A 和 B
2 Work hard and you will be successful. 努力工作，（然后）你就会成功。
In this sentence, successful is a result of working hard. You don’t need to translate “and” here（just put a comma here to separate the two meanings）, If you insist, you could translate into “然后=then”, this will show the relationship between “work hard” and “be successful”.