There are multiple ways that you could solve your problems. I will only present one way for each.
1. Because you said you had a time stamp, sort the data by product (which I called Group in my formula) and then time stamp (in ascending order). Now create a formula that looks like this:
With this new column, select all of the 1's (select one, right-click and select all matching cells). Choose Tables > Subset.
Or, you could select all of the 0's and then choose Rows > Hide and Exclude, depending on if you might ever want to see the other data.
For question #2, 50 product is a large list so there will always be some work. But you could use the same approach and build a formula that returns a value of 1 if your product is in the list and 0 otherwise. That If statement would be large though because of the 50 values. (it would be IF product=A or product=B or product=C, etc...). You could also use the Match function, which would be more efficient for JMP to evaluate.
But for this question you might also be able to use a Local Data Filter to interactively select which product(s) you want to see.
You might want to go through some of the beginner tutorials made available under the Help menu of JMP. Those can give you a good start on how to do some of the basic data manipulation features available in JMP.
Dan Obermiller