1)跟他在公司打拼奋斗。
Struggling for work with him in the firm/company.yes, you are right. Just 打拼 or 奋斗 is enough. It is not for emphasis on 奋斗, and 打拼=奋斗 here. Like "There are monkeys and monkeys and monkeys on the monkey Island", Just for 强调。
2)我并不是不告而别。
不告而别=bundle off/ desert/ leave(go away)without say goodbye.
而别 is not a phrase, 而=when/while.
3)完全没办法乘虚而别。 It's wrong, I guess you want to express 乘虚而入,It's a idiom.
Take a advantage of a weak point into.
swoop in.
get a chance to step in.
完全没办法乘虚而入=There is no way that you/sb can 乘虚而入。
4)你让我情何以堪哪?
How should I get?
Can stand?
what could I do?