The 90 day clock starts when you arrive in mainland Europe.
The UK isn't in the Schengen Area, so your time there has no effect on your Schengen time limit.
It's worth noting that the EU and Schengen Area, while related, are different things: several countries (UK, Ireland, Bulgaria, Romania, Cyprus, Croatia) are in the EU but not Schengen, while some (...
Your stay in the U.K. does not count towards your Schengen stay limits. They are completely separate visa regimes.
Even if you stay for a whole 6 months in the U.K., it still is 0 days in the Schengen area.
Your proposed plan is perfectly fine. Your 90 day Schengen limit will start when you enter the Schengen zone, not when you enter the U.K.
As noted on the Department's web site on the Working Holiday visa:
Stay longer on a visitor visa
Generally we don't grant a visitor visa after you have been in Australia on a Work and Holiday visa.
If you want to apply for a Visitor visa to stay longer in Australia and the Visitor visa would result in you staying longer than 12 consecutive ...
You should think less in terms of "The rules say I can enter Singapore for 90 days" and more in terms of "The rules say the immigration officer can allow me into Singapore for up to 90 days." 90 days is allowed because it should be enough for the vast majority of tourist or business visits.
If you want to stay longer than 90 days (and staying for 80 days, ...
If you were admitted for six months, you can stay for up to six months. You don't need to inform anyone. Even if you want to do so, you will have a hard time finding anyone to accept that information.
You can check your period of admission at https://i94.cbp.dhs.gov.
However, given your earlier visa refusal, you should be careful. It's possible that ...
In addition to telling what she will be providing you with, you must document that your sister is legally resident in the UK.
Also, since she lives in rented accommodation, she must show that her landlord is okay with her boarding guests -- either in the form of a lease that explicitly allows this in general, or a letter from the landlord that permits it.
You are a student.
Skip such document, and add a document that states that you are enrolled to a Canadian University, and that you will start in September.
Never lie, answer the most honest as possible. If the form seems wrong, ask here, or add a note about your interpretation.
I don't believe an Indian official should have much knowledge of UK's Immigration Act 1971 nor of the Immigration and Asylum Act 1999.
Additionally, I don't believe an Indian official would be authorised by UK's Secretary of State to make declarations on UK's Secretary of State behalf.
Based on the above, I would argue this is for UK's representatives.