When a bond issuer calls a bond, they give a notice, typically 30 calendar days, but sometimes 45 or 60 etc. The number of notice days can usually be found in the bond's prospectus.
The calls can be European (callable on one date), Bermudan (callable on a list of dates, which usually coincide with coupon dates), or American (callable on or anytime after some date).
Bloomberg has a "call days" field, but inconveniently leaves it blank if it is 30. When you copy data from Bloomberg to your local database or spreadsheet, you should replace blank call days by 30 for callable bonds. So, for example, if you're trying to find the yield to worst for a bond that has an American call, you should assume that the bond can first be called after "call days" days.
The coupon accrual stops on the call date, not when the call is announced, not plus-minus any days to settle. There is usually less liquidity after call announcement, but the bond still trades, at price close to call price. There usually isn't quite any bond left to trade after the call date. The call date works very much like maturity date.
A bond call price is usually the fixed clean price (usually just par, sometimes par plus the remaining coupons) so the bond holder receives the clean call price plus the coupon accrued until the call date. But sometimes make-whole calls get exercised too. For a make-whole call, the dirty price is going to be calculated on the call date by observing some treasury (usually on the run 10 year), adding some spread specified in the prospectus, and using this to discount the remaining cash flows of the bond. Their present value will be the call price. Inconveniently, Bloomberg just leaves the call price field blank for make-whole bonds, so you should calculate it yourself (keeping in mind that it is an estimate that will change every time treasuries move).