Is it ok to use a slash to separate alternatives, as in "If 1st_method/2nd_method is used and 3rd_method exists....", in academic paper writing?
Strictly speaking yes it's "ok" but it does not mean it's the best.
Most style books (I'm looking at AMA Handbook at the moment) would list that using forward slash (also called virgule or solidus) to represent "or" is acceptable. But the same symbol can also represent "and" as well as "per." So, there is some chance that misunderstanding can arise.
If it's not under strict word limitation, you may consider using the word "or" in between the two named methods.
What is wrong with something like :
If either the first method or the second method is used...