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英語で意味は何ですか。

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.