1. Generally you want to see both: higher close, higher intraday high. You want to see a healthy uptrend which includes pullback that do not violate previous lows.
2. If it breaks some resistance and makes a higher high, then it is in an uptrend (how strong of an uptrend is a case by case evaluation). You should be able to buy the breakout as well as the test of the old resistance/new support. But honestly in this market you should not really be buying ANY breakouts. If you time these entry intraday and get good prices, then stops are much easier to set.
3. I wouldn't focus too much on volume. High volume days CAN signify turning points and it is best to see increase in volume in the primary trend and decreasing volume on pullbacks. But remember, ff a stock moves up 10% on low volume or high volume, it has still moved 10%! Here is an article on volume
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