correct

No, it isn't necessary.

Yes, gel electrophoresis separates fragments based on their size. Therefore it will be able to separate a 200bp fragment from a 400bp fragment provided you use the correct gel composition (as this affects the sensitivity to size differences).

paint the base blue and then fill it with hair gel or clear glue

Yes you can apply relaxer to new growth if your hair has gel in it. If you used a hard gel normally your hair will be hard. Try parting your hair using your hands on four sections. Then apply the relaxer to new growth only, once the relaxer is applied it makes the gel in your hair softer by breaking it down. After applied evenly you can use a comb to smooth the rest of the relaxer process, going back through making sure you applied the relaxer evenly. Hair gel is also used as a base or can be used as a base as most hair gel such as ampro is protein.