Is it ok to rely on lots of third party packages?
Well, I think this a lot based on your opinion. 
Personally I would say it's a good idea to use a lot of third party packages. It enables you to develop faster and why inventing the wheel all over again?
Advantages:

faster development
DRY, don't reinvent the wheel
higher likelihood that the tools are time-tested and have bugs worked out (@erip)

Disadvantages:

support of third party packages could be dropped.
sometimes they don't fit your needs exactly
if open source license changes, you're suddenly without support or liable to a legal battle (@Sayse)
My organization uses django for our website so we have the opportunity to use pypi packages, but we don't seem to have used many in the past and developers have written there own solutions instead. I've always used lots of packages in my own project. Is there really any downside to using these packages?