Question 179190
Your answers are correct so far.
You did the hardest part already. 
{{{y[M]=2x+1}}}
{{{y[N]=-2x+1}}}
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B) When the lines intersect they have the same y values. 
Set the equations equal to each other and solve.
{{{y[M]=y[N]}}}
{{{2x+1=-2x+1}}}
{{{4x=0}}}
{{{x=0}}}
Then use either to solve for y.
{{{y[M]=y[N]=2(0)+1=1}}}
The intersection point is (0,1).
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Graphing the two lines might help visualize what's going on. 
{{{drawing( 300, 300, -3, 3, -3, 3,grid( 1 ),
circle( 0, 1, .1 ), 
circle( 1/2, 0, .1 ), 
circle( -1/2, 0, .1 ), 
graph( 300, 300, -3, 3, -3, 3, 2x+1, -2x+1)) }}} 
Line M in red and Line N in green.
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C)Line M intersects the x axis when {{{y[M]=0}}}.
{{{2x+1=0}}}
{{{2x=-1}}}
{{{x=-1/2}}}
Line M intersects the x-axis at (-1/2,0).
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Line N also intersects the x axis when {{{y[N]=0}}}.
{{{-2x+1=0}}}
{{{-2x=-1}}}
{{{x=1/2}}}
Line N intersects the x-axis at (1/2,0).
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D) Line M intersects the y axis when {{{x=0}}}.
{{{y=2x+1}}}
{{{y=2(0)+1}}}
{{{y=1}}}
Line M intersects the y-axis at (0,1).
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Line N also intersects the y axis when {{{x=0}}}.
{{{y=-2x+1}}}
{{{y=-2(0)+1}}}
{{{y=1}}}
Line N also intersects the y-axis at (0,1).
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Here's a case where graphing the lines really help visualize what's going on.