If your contract is silent on whether the extra holidays are calculated pro rata then you can assume that they are as that is the accepted method. In your case if you have been there for 3 months of this holiday year, you would be entitled to 5.5 days for that period. If you have already taken 10 days then your employer can deduct 10 less 5.5 days = 4.5 days holiday, which they have done.
As for notice then you are entitled to your contractual notice period. If they requested you to leave after 4 days then you are entitled to be paid your remaining notice period in lieu of notice. Your employer can only do that if your contract allows them to or if you agree to it.
I also assume you are working part-time as the minimum holiday entitlement for full-time workers is 28 days.
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