Probate is the process of applying to court to have the executor's appointment officially approved by the court.

If there's no will this confirms that the executor has authority to administer the estate. If there is a will, probate confirms that the will submitted is the last and valid will of the deceased.

The probate certificate is now called "Certificate of Appointment of Estate Trustee."

Probate forms can be hard to fill out if you don't know what you are doing. I can help.

No. There is no legal requirement to get probate, but 3rd parties like banks and the land titles office usually insist on it to transfer assets. Everyone is interested in covering their own behind, and probate is the best protection they have that the executor telling them to transfer assets is the legal executor.

Some assets don't need probate and you can plan around probate with the right advice and specialized wills.

The easiest way to know for sure is to ask an experienced estates lawyer like me.

For the privilege of having the court stamp the certificate, it costs roughly 1.5% of the value of the estate. It's not huge, but it certainly can add up. But not all assets go through the estate (some joint property, registered plans or insurance with designated beneficiaries). If in doubt, get legal advice. The government now audits probate tax filings, so be careful.

Probate tax is now called "Estate Administration Tax."

Yes, so long as the will doesn't say "no compensation." The will can fix compensation, but if it's silent on the point, the general rule of thumb is executors are entitled to be paid roughly 5% of the estate value for their trouble, care and skill. It's a lot of work and risk - they deserve it (and they have to be pay income tax on it)!

If there is a back-up executor named, they can apply for probate. If not then someone else can apply with the consent of the beneficiaries.

You can formally renounce and wash your hands of it. Just don't start doing the job and then decide you don't want to do it. Once you've started, it's hard to get out of it.

Many times it is better to have a professional act as executor despite what the will says. The named executor can renounce and the beneficiaries can consent to the professional's appointment.

Legally no, practically yes. 

If you live anywhere in Canada or another Commonwealth country you can still apply for probate no problem. But if you live in the US, it might be a good idea to renounce and appoint a local executor (like a professional). Non-Commonwealth executors have to post a bond with the court (~ 2x the value of the estate) as part of probate. 

Aside from that, being an executor involves a lot of legwork and is much easier if you live in proximity to where the deceased resided. Think long and hard about travel and your own time. It's usually worth it to find someone else to do the job.