Finding resistance and how many appliances can be connected
If you were marked wrong on the first question, it may have been because you seem to be pulling an arbitrary value out of nowhere that leads you to the correct answer.  You should also show and process units at the middle stages of your calculations, as doing so can help prevent numerous errors, aid in communication with your peers and improve your understanding of what equations mean.  Instead, they probably would have liked you to write:

Given:
\$E=240V, I_{MAX}=16A, P=EI\$
Solve for \$P_{MAX}\$
\$P_{MAX}=E*I_{MAX}=240V*16A=3840W\$
\$3840W/1000W=3.84\$
3 devices can be connected.

If you use this structure for your answers, you will likely greatly increase your success in math and engineering classes.  State your givens, use good or accepted variable names, always include units until they properly cancel out.  In answering a question, you are attempting to prove you knew how to solve it, so even if the answer is correct you will miss marks if it appears you arrived at it by coincidence.  Many professors/teachers will give marks for correct answers derived in unexpected ways, but at first glance, it is not remotely clear where you pulled 57.6 from.  I looked at it a minute longer and OK, you found resistance, calculated current per device and divided total current by that, which is a bit more roundabout, but correct.  Include your units and your answer should be fine, but note how easy it is to understand my answer at a glance.
Your answer, using Ohm's law(\$E=IR\$) and Kirchoff's current law(\$I_{TOTAL}=I_1+I_2+...I_N\$), is correct, however less direct that using Watt's law(\$P=EI\$), so perhaps you should brush up on Watt's law or try to be more aware of it, unless in this module they prefer you to solve in the way you have.
Your second answer I'll just rewrite with more clarity

Given:
\$P=1000W, E=240V, P=EI, E=IR\$
Solve for R
\$I=E/R\$
\$P=EI=E(E/R)=E^2/R\$
\$R=E^2/P=(240V)^2/1000W=57.6\Omega\$

Just an example.  Definitely start showing your units, although you can likely get away with showing less algebra than I have, if you get in practice doing this during your early education it will greatly help you throughout.  Nothing will ever force you to do it when you don't have the time, but when you do it will really help you with math courses.  Good job though, you are correct.