Is it normal that occasionally Page Life Expectancy drops to 0 and queries start giving timeouts in SQL Server? Can somebody shed some light on if it's normal that Page Life Expectancy drops occasionally to 0 in SQL Server (2014) resulting in slow queries and timeouts?

I'm facing this on my developer machine when developing a web application and I don't know whether it is because of the development environment or something else. PLE may be over 10000 for one day or a couple of hours (during which queries work fast) until it drops to 0 and all my queries go from 15ms to 40 seconds or more.

I mean is there any way to control the performance of SQL Server in this matter or is this by design of the SQL Server that it may get slow, for example, due to memory pressure until it comes faster again etc.? 

To me it looks like queries are read in a cache and at some point they're flushed out and queries start giving timeouts because everything is read from a disk. Is this something that can be avoided?
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.