あんまり = あまり is a noun formed from the verb あまる (余る) meaning 'to exceed'. It can mean 'the excess', 'the surplus', 'the rest', as well as 'excessively', 'too (much)'. Example: あまりに悲しくて泣き出した "She was so sad that she started to cry". However, usually it is used in negations which generally looks like this: あまり....ない (not too .... / don't .... too much). Example: 私は魚があまり好きじゃない　"I don't like fish too much". こういうの慣れてないですけど　"I'm not used to this kind of things (but)" - 'but' is optional because not knowing the rest of the dialogue, I can't judge if けど here really means 'but', or if it's just a way of finishing the sentence (common in spoken Japanese). それでも大丈夫ですか "Is it fine (even if it's) like this?" Hope this helps.

You are welcome. Your question and Karol's answer help me a lot!

Thanks Ryoko :)

Hi Roro, I also want to know how to say them in English. あんまり＝あまり, but あまり is more formal. (not very, not quite, not many, not ~ too ~) Ex.) I don't like this movie very much. 私はこの映画があまり(あんまり) 好きではない。 Sorry that I can't help with other sentences. Hope you get great answers.