In the end you will probably will want a BB-buzzer to be heard (or a BB-pop-up).
Not really.
Maybe its just me but I have my speakers turned off unless it is absolutely necessary to have sound in order to minimise noise pollution and to conserve electricity. If you're watching a movie or playing a game and there is sound then fair enough, but to have a sound that will only pop up once on the trigger of that event is totally useless to me.
Setting an actual alarm on my phone actually serves better than having a noise that could potentially go off on my computer when speakers are off anyway.
This reminder will be sent several times during an auction, as there are many bidders (usually).
Again, your idea is absurd. As stated previously you only need to be online 5 minutes before the player's scheduled auction is to end. Bidding any earlier is a total waste of time. You will spend maybe 15 minutes at around the near end of the player's deadline but you would be too busy refreshing the player's page every minute or 2 that you won't be doing other things.