You asked about whether the following three sentences mean the same:
1)Your English will GET better and better.
2)Your English will BECOME better and better.
3)Your English will BE better and better.
The three sentences above have the same meaning, but when we want to express an action with "better and better" (meaning to grow progressively better, little by little, not al at once),then we usually use either "get" or "become". Both of these verbs, but not "be"(in#3), are for talking about change."Because" can be used to replace "get", but instead of replacing"get", you should just use it, as natural, idiomatic English uses this word very often.