Is the blue conduit connected to my sub-panel suitable for a 50A branch circuit?
Smurf tube.  The name its mom uses to yell at it is "Electric Non-metallic Tubing" or ENT. 

You will need to run a separate ground wire since it is not metallic.  

You have to watch out for conduit fill, there are fill calculators on the web.  

If you plan 4 or more circuits in that conduit, come back and ask us about derating, but you probably won't have space for that.



DIYers must be careful when designing conduit pulls.  Too difficult a pull requires an electrician's truck full of pulling tools, and the owner of that truck typically will only agree to do the whole job. 

Most people go straight for multiconductor cable because that's what they know.  Meet THWN-2: it is an individual wire with a special jacket made for pulling. It is typically stranded and much more flexible than cable. Conduit pulling is much easier. But it lacks the armor of cable so it cannot be used outside conduit. 

So you have 3 choices: a) cable all the way including through the conduit, b) extend the conduit (using any conduit type) to your destination and use THWN-2 wires, or c) THWN-2 through conduit to a junction box, there splice to a cable. Any of these are a compromise on difficulty.  

I would extend the conduit just because that's my better skill.