hood struts for chrysler LHS 2001

yes

unless you want the hood to fall on your head.

Both and then you need an alignment after. Might be a good time to do the brakes too. Check the short axles etc.

If these are the original struts, yes. If they've both been replaced, but a while ago, yes. If you got a pair in the (very) recent past and one has failed prematurely, no.

The basic point is that they're a set, and if one has failed the other is really weak (to the point where the distinction between its current state and failure is probably pretty academic). Rarely, a strut will be defective and will fail long before its twin. Rarely.

if you bought cheapies at a discount auto store its not unheard of them failing sooner than expected too. I had a pair from AutoZone at 18.00 each, last less than 2 years.