Well, it's a fiction -- a crowd-sized delusion, packed with 90% myth and 10% fact. As time bears on, and tests and retests come and go, the myth gets examined, the facts get reinforced at a different level, and with each approach, the likelihood of a breach increases. S/R are a sandcastle against a market tide -- it might hold for a wave or two, but jeeeeez, don't rely on it. Show me S/R that held after 4 approaches, and I'll show you an S/R that was breached on the fifth.
Arguments both sides. Not relevant for the trade. The only thing that matters is whether "S/R appears to have held/broken this time". (Recall years ago an index testing resistance 22 times on its daily chart before it finally broke.)
It's better, in my opinion, to check S/R across different time frames as opposed to one time frame in isolation.
The question doesn't adequately address the importance of S/R. Just because it was tested 3 times doesn't tell you about its strength. There are other factors like how often the S/R was tested and what the severity of the (price) momentum was. For example, if S/R withstood the onslaught of a strong momentum, then the likelihood of a reversal is very high.
Many trading patterns consist of trendlines that break. Prior to the break you could make the argument that each touch made it weaker which eventually caused it to break. If the trendline had many touches prior to the break, it will likely make a strong move on the break of the line (many SL hits) and will likely be harder to break now from the opposite side. So prior to the break, each touch made it weaker but after the break, the greater # of touches makes it stronger from the opposite side.
Day trading wise.... 2nd bottom likely bounce, no retail trust to kill 3rd bottom likely fail as retail will spot and trust 3rd must be better than 2nd. Market will do what is worst for retail on purpose to take our money.