Are we using "to jest" (rather than "ten jest" or "ta jest" because jajko is neuter? or is the form always "to jest"?
To jest = "it is" or "this is". Always. There is of course also "ten jest", but it translates more or less to "this one is".
So "ta jest" means "this one is..." then followed by a feminine nominative noun?
"Ta ryba jest duża. Ta jest mała." = "This fish is big. This one is small".
Or let's say "Ta rzecz jest książką. Ta jest jajkiem." = "This thing is a book. This one is an egg."
Generally it's not something you use often.
Why is jajko not in the instrumental case?
You need to remember that after to jest you use the nominative case, hence to jest jajko.
Why is "It is an egg" incorrect?
It's correct and accepted, it should have worked.
Why "This is egg" is not correct?
Eggs are generally countable, and for the rare examples when it could be treated as uncountable we would probably specify it further.
What Is the difference between "ten" "to" and "ta"?
"ten" is masculine
"ta" is feminine
They all have to agree with the noun they describe in terms of grammar.
"to" is neuter