Upvoted because these are good questions, indicating a genuine willingness to understand exactly what another poster is saying. That’s the kind of discussion that I come to Hacker News for. Not everyone has the same background and understanding of terminology and they shouldn’t be down-voted for that.

A "group" is a bundle of atoms that hangs off the side of a core structure, typically. http://www.chem.ucla.edu/~harding/IGOC/G/group.html

When you do a reaction on a chemical, the reaction can often affect multiple different parts of the structure, even if you only want it to affect one site. So, you can pop a "protecting group" onto the site you don't want modified, and then remove it later. https://en.wikipedia.org/wiki/Protecting_group

A TA is a teaching assistant; typically a grad student with lots of knowledge teaching a class to undergrads.

You would want to characterize any synthesis- verify your work to make sure you got high quality product that is pure.

The 'groups' are chemical structures present in a compound. The student asks the Teaching Assistant (typically a graduate student who is required to do teach) a general question about how to carry out a multi step process to selectively transform specific regions of chemical compounds.

The punchline is that the Teaching Assistant immediately sees the intent of the question, and goes from the general to the specific and replies: [ you won't be able to synthesise LSD with that approach because ] "all of the precursors are also scheduled."

Leaving groups are the part of the molecule that are designed to "leave" during a particular reaction

https://en.m.wikipedia.org/wiki/Leaving_group

You design your synthesis around this and try to pick pathways that are easy, have the highest yields, and don't produce undesirable products you have to remove.

I'm guessing TA is teaching assistant.