Day Trade $25,000 again

Some clarification first because it is not clear how many day trades you made and in what time period.

You can only trade settled cash in a CASH ACCOUNT. That means that with T+2, the funds from a sale will not be available for two days. There is no limit to how many day trades you can make in a cash account as long as you are using settled funds.

A pattern day trader is a person who executes 4 or more day trades (options and equities) in a rolling FIVE business day period in a MARGIN account, provided the number of day trades are more than six percent of the customer's total trading activity for that same five-day period. If you are a pattern day trader then you are subject to the $25k minimum.

case 1: If I buy $10,000 worth of stocks in the morning, only $15,000 cash left, the above account still meets the $25,000 requirement, right?

You meet the $25k requirement as long as the value of the stocks do not drop.

case 2: If the stocks go down in the afternoon, at the end of the trading day, that $10,000 worth of stocks only has a $9,000 market value, the above account will get a call/warning about the $25,000 requirement, telling me that account needs more cash?

That is correct. You will be restricted from further day trading until you add cash or marginable securities, restoring the $25k minimum.

case 3: If I spend all $25,000 cash on stocks, now no cash left, but the market value of these stocks is above $25,000, does the above account still meet the $25,000 requirement? how about if the market value is less than $25,000?

This question is just combining the questions asked in case 1 and case 2. The same answers apply.