touch base

to talk to someone for a short time to find out how they are or what they think about something    聊聊；谈谈（和某人短时间谈话，了解他们怎么样或他们对于某事的想法）

I just wanted to quickly touch base with you: did you get an email from my secretary about the meeting?   我只想和你简单聊一聊：你收到我的秘书发给你的一封关于这个会议的电邮吗？

I don’t think I have ever conveyed adequately my gratitude in your mentorship

可以适当省略主语，例：Would love to have coffee with you sometimes if you have 20 minutes.

I dream to work for an energy start-up with which I wholeheartedly share the vision.

Thank you very much in advance for your time and insight.

... has made you an icon-like figure among us interpreter going-to-bes

I know that... 可以替换为I do understand that...

a simple 10-15 minute talk over coffee

I understand that Andrew's schedule is probably very tight: hence any amount of help he can give is very much appreciated. 凸显出诚意

the other day 前几天

hear from sb phrasal verb

If you hear from someone, you get a letter or telephone call from them, or they tell you something

reach out to sb phrasal verb

1 MAINLY US to try to communicate with a person or a group of people, usually in order to help or involve them 用来替换contact, communicate
2 to offer help and support to someone

Thanks for the well-thought-out course blueprint for Academic Writing. 形容词  经过周详之考虑的

Just trying to check in with you regarding where we are on (where we are， 真的就是很地道的描述“我们做到哪一步了”的地道英语说法) that project.

Also I am thinking（I am thinking比I think会更柔和，更有商量的意味）

deadline是吓唬人来加速干活，而优秀的可能性则能激励人们加速干