Learning and doing other activities on Erev Shabbos

Doing work on Erev Shabbos and Erev Yom Tov

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Yes, as is the ruling in Shulchan Aruch, which is binding on all Jewry without exception, and thus the question itself is most puzzling. In fact, the Alter Rebbe was so particular in this matter that he writes that one who doesn’t follow it will be banished from having audiences with him.

Sources: See Admur 102:5; Shut Admur 12 Takanos Tefila and Takanos Liazna

How important is it to give an exact report to the insurance company, and may one exaggerate expenses, or not report negligence, in order so the insurance covers more costs?

It is biblically forbidden to do so due to the stealing prohibition, whether the owner of the company is a Jew or Gentile. One must give an exact report to the company, and may only receive reimbursement for money that he is entitled to under the contract, based on the true events that occurred.

Source: See Admur C.M. Hilchos Gezeila Ugineiva Halacha 1-4