Does this mean I need to notify CIC every time I need to visit my home country, or travel to attend conferences, etc. for over 2 weeks in a row? Even the travel is temporary?
yes, if you are going for more than 2 weeks in a row then yes because they won't schedule any test or appointment for you during that time.
If you go without telling them and in your two weeks absence you receive a letter asking something like test, additional documents and if you miss the deadline for submission then it will be big trouble for you
There is no hard-and-fast rule for this, but, in general, the sooner the better. The CIC typically gives between 1 1/2 weeks to a month notice of a test or oath.
If you haven't gotten a test invite yet, no, you won't have to reschedule. Just inform CIC of the trip when you book your ticket.
If you miss a test or have to reschedule (rescheduling is tricky), yes, your application will probably be delayed a bit. How much? No one can say. Will it happen for certain? No one can say.
It's best to follow the instructions. Inform CIC. If they delay sending you the test invite for 3 weeks, it's not a big deal. You've got to live your life. But be smart and follow the instructions.
I heard the oath date cant be re-scheduled and is set in stone. So lets say I informed CIC in advanced and if after taking the test, I travel to India to attend the wedding and then the Oath date is announced and if I am in India at that time, will it be a problem?
Not worried about residency at all. This country is our home and we have been living here since arrived.
No, it can be rescheduled. You just need a good reason and to inform CIC ahead of time. A wedding sounds like a good reason. But the people I know who were able to reschedule already knew their oath date. Not sure about people who told CIC in advance that they are unavailable before they got the oath invite letter...
I heard the oath date cant be re-scheduled and is set in stone. So lets say I informed CIC in advanced and if after taking the test, I travel to India to attend the wedding and then the Oath date is announced and if I am in India at that time, will it be a problem?
The purpose of informing CIC of travel is so they don't schedule you for an event while you're away. Other than that, they don't care when and where you travel as long as you meet your PR residency obligation.
If they schedule you anyway, that's something you can deal with in the future. It's really not something you need to game out now. If you're really worried about it, make sure to either inform CIC of any travel dates in writing, keeping copies for yourself. Include your UCI and file number in any correspondence and send it with a tracking number and signature requirement.
Otherwise, just keep a log of your CIC Help Centre calls, noting the date and time of your calls, the name of the agent and what was said.