Some caching plugins that cache entire pages or sites in
.html files so obviously anything generated on a page will be "cached" in that file. Other kinds of caching stores information in memory (RAM). The answer differs some according to which kind of caching you are talking about, but...
If I use transient api is it required caching plugin? (I hate plugins!!!)
Don't hate plugins, just avoid the bad ones.
You don't have to use a caching plugin, ever, if you don't want to. Without a caching plugin you still get a kind of database-based caching.
If I use transient and caching, how will be the result?
A caching plugin should store transient data persistently in memory (RAM) which allows faster access but obviously uses more RAM.
Can I use transient against caching plugin?
No idea what this means.
Is caching plugin and transient work on same principle?
Depends on the kind of plugin, I guess, but probably not. The transient API saves data to the database. By saving "heavy" work like a complex query or a remote HTTP request to the database you can get at it faster on subsequent requests. A caching plugin will save that data in RAM or a file which should likely be faster than PHP/MySQL.