Where to stay in Paris for easy access to Palaiseau?

I will attend an event at Ecole Polytechnique in Palaiseau from Monday to Friday. The event will take place between 8am to 10pm, but some days it takes shorter (like until 5:30 pm). I may also have the weekends free before and after the event, so it is also a chance to see Paris.

Should I stay in Paris or in the suburbs (like Palaiseau, Massy, Saclay) close to Ecole Polytechnique? If the event ends at 5:30pm I will want to see the city, eat/drink, etc. I need to find a place that is safe and easily accessible by public transport to stay low on budget. Unfortunately budget is a concern for me, I only have 50-80 Euros for a night for accomodation.

Schengen visa refused using motif 2 on purpose and conditions of stay

A friend of mine who is an official teacher, applied for a visa to Germany and got refused because of the motif #2 saying:

The purpose and conditions of the intended stay have not been established 

The file was full of papers, the original invite from her son in law was in the file, and even a high amount of money in the bank account.

What is extended explanation of this motif and how can she pass it in her next apply.

Re-enter Schengen with a residence card

I checked related questions, but they are more about visas, which is slightly different from my case.

I am a Chinese citizen holding a residence card in Norway. I have only a single entrance Schengen visa which has expired earlier this year. I plan to attend a conference in Ireland and a course at Svalbard. As Ireland and Svalbard are not Schengen area, I will leave Schengen area and re-enter when I come back. I am wondering if it is enough for me with my residence card, or if I need to apply for a new visa to enter Schengen area, (in my case just Norway)

How long can I stay in Europe as an EU citizen living in the US?

I am a dual citizen (US/Greece) currently living in the US and visiting Greece for three and a half months. I entered Europe through Germany using my US passport (the Greek one is in the process of being renewed) and was told I could only be in the Schengen area for 90 days.

Am I legally allowed to stay in Greece as long as I’ve planned (~105 days), given that I’m a Greek citizen? How do I justify this to officials when returning to the US?