Can day/week traders take profit from Volatility only?

Under most circumstances, if you own a one month $60 call and the stock moves up $1 in one day, you're not going to make any money. This is because the delta is very low. Add to that the B/A spread and it's even more unlikely.

Yes, you can find outlier situations where the implied volatility is sky high and the $1 move generates a profit (10-15-20 cents) but with such high IV, the B/A spread is going to be huge.

Profiting from volatility requires much more than basic option knowledge because the strategies are more complex. For example, selling high IV straddles/strangles before an earnings announcement. This is high risk. For something tamer, selling nearer term expensive high IV options and buying cheaper IV next week or two out options.