Now, my question is, is it enough to show the PR number (of sibling) when applying for express entry, or do we have to prove that sibling is currently staying in Canada?
She can take trips outside Canada, but her principal residence must be in Canada as proved by e.g. rental lease, bank accounts.
PR number is not enough in any case. You need to submit at least a scan or copy of her PR card (both sides).
To claim the sibling points, you need to provide
A copy of both sides of the family member's Canadian citizenship
document, Canadian birth certificate and/or permanent resident card
must be provided.
Evidence that the family member currently resides in Canada must be
provided (a residential lease, mortgage documents, utility bills,
etc.). The documents must show their address in Canada and should be
recent (dated within six months prior to submission).
Proof of the relationship of the applicant or the accompanying spouse
or common-law partner to the family member must also be provided
(e.g., a birth certificate, an official document naming the applicant
as a relative, a copy of the inside back cover of the relative’s
passport showing the relative’s parents’ marriage certificate, legal
adoption documents and any other documents that prove or describe the
relationship).
If the applicant claims a stepbrother or stepsister, there should be
no evidence in the application that the marriage or common-law
relationship between the parents of the stepbrother or stepsister has
broken down.
https://www.canada.ca/en/immigration-refugees-citizenship/corporate/publications-manuals/operational-bulletins-manuals/permanent-residence/express-entry/applications-received-on-after-january-1-2016-completeness-check.html
You only need to provide these documents when you receive an invitation to apply.
my second question is - "I am working for the past 12.5 years and last month I changed my job and joined a new company. Now, I have got a much better offer from another company and for that, I would have to abscond (i.e. with no reliving letter) from the current company. So I won't have any proof of job for this 30-40 days. Will it affect my visa application? Is it mandatory to not have any gaps in jobs when applying for an express entry visa in Canada? "
A couple of months of unemployment is not a cause for concern. But the amount of work experience claimed need to match what you actually did and can prove.
