Is it normal that occasionally Page Life Expectancy drops to 0 and queries start giving timeouts in SQL Server?
If your laptop has 4 gigs that means that SQL Server probably has access to 500 megs of RAM at best. 

PLE tells you how long SQL Server is able to keep data in memory. If there's no load on the SQL Server then the PLE will just keep climbing. Once you put load on it again the PLE will drop as the SQL Server needs to read data from disk. The more data that it needs to load from disk the longer the queries will take. 

If your disk is slow, which it probably is in your laptop the queries which hit the disk will just run slower as you want for the disk to spin. 

If you want good performance on your laptop you'll want to ensure that SQL Server has enough RAM to ensure that the working set of your data sits in memory and not on disk. The first time it is accessed it'll need to be loaded from disk but after that you want it to stay in memory. You'll probably want an SSD as well so that the disk is fast enough.