1. does 馬屁 mean something like "bullshit?" what about 拍馬屁? to fawn or curry favor with? to "kiss up" to someone?

Bullshit is more like 放屁!(expressing your disagreement, dissatisfaction, or anger)
Yeah, 拍馬屁 refers to the way one curries favor with his/her boss or superior; maybe with designed behaviors or sweet speech.
Some more slang usage may be as following:
ex:
你是超級馬屁精! You are such a brown nose suck up!
你在拍馬屁喔! You are buttering up! = You are sucking up! =You are flattering!
你是馬屁精! You are an ass-kisser!


2.【這也不見得能難得倒我】what does this expression mean? especially the last part 難得倒我?

Literal translation:
This (job) may probably not be able to cause difficulty for me.

Free translation:
This (job/task) will be just a piece of cake for me. (=I think I can handle the situation if I try my best. 迳 the speaker is confident about his own ability to solve the problem)

難得倒我 can be "a trouble/problem for me" or "Got me"
ex. 這個題目不一定難得倒他，因為他是個天才！
(This problem may be just a piece of cake for him to answer cause he is a genius!)


3.【這位前輩一副孺子可教的神態...】does 孺子可教 mean teachable?
and 神態 mean attitude, composure?

Literal translation:
This senior showed an expression that he thinks I am a young man worth to be taught.

So yeah, 孺子可教 refers to the status that a young person who is teachable, with potential and talent to be a good student.

And 神態 actually means expression and attitude. 时