Enhancing a plot

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Consider the following code.

f0(x)=3-x
f1(x)=2*x-6
f2(x)=1+(1/3)*x
p=plot(f0(x),x,1,3.5,thickness=3)
p+=plot(f1(x),x,2.7,4.5,thickness=3)
p+=plot(f2(x),x,1,4.5,thickness=3)
sol0=solve(f0==f1,x)
sol1=solve(f0==f2,x)
sol2=solve(f1==f2,x)
p+=point((sol0[0].rhs(),f1(sol0[0].rhs())), rgbcolor=(0.26, 0.80, 0.50),size=60, zorder=10,axes_labels=['$x_1$','$x_2$'])
p+=point((sol1[0].rhs(),f2(sol1[0].rhs())), rgbcolor=(0.26, 0.80, 0.50),size=60, zorder=10)
p+=point((sol2[0].rhs(),f1(sol2[0].rhs())), rgbcolor=(0.26, 0.80, 0.50),size=60, zorder=10)
p+=point((0,f2(sol2[0].rhs())), rgbcolor=(0.99, 0.86, 0.23),size=60, zorder=10)

p+=point((0,0), rgbcolor=(0.99, 0.86, 0.23),size=60, zorder=10)
p+=line([(0,0),(0,f2(sol2[0].rhs()))],rgbcolor=(.5, 0.5, 0.69),thickness=3, zorder=8)
p+=point((sol1[0].rhs(),0), rgbcolor=(1, 0.1, 0.5),size=60, zorder=10)
p+=point((sol2[0].rhs(),0), rgbcolor=(1, 0.1, 0.5),size=60, zorder=10)
p+=line([(sol1[0].rhs(),0),(sol2[0].rhs(),0)],rgbcolor=(1, 0.5, 0.69),thickness=3, zorder=8)
p+=polygon([(sol0[0].rhs(),f1(sol0[0].rhs())),(sol1[0].rhs(),f2(sol1[0].rhs())),(sol2[0].rhs(),f1(sol2[0].rhs()))], rgbcolor=(0.9098, 0.3804, 0))
p+=text("$\\mathrm{Points }\\,\\, \\mathrm{intérieurs}$",(2.8,1.2), color='white')
p+=text("$x_2=3-x_1$",(1.9,.6),rotation=-44.0, horizontal_alignment='left')
p+=text("$x_2=2x_1-6$",(3.5,1.2),rotation=62.0, horizontal_alignment='left')
p+=text("$0$",(-.15,0.1), horizontal_alignment='center',color='black',fontsize=12)
p+=text("$x_2=1+(1/3)x_1$",(3,2.2),rotation=16.0, horizontal_alignment='center')
p+=line([(sol1[0].rhs(),0),(sol1[0].rhs(),f2(sol1[0].rhs()))],linestyle="--",color='black')
p+=line([(sol2[0].rhs(),0),(sol2[0].rhs(),f2(sol2[0].rhs())), (0,f2(sol2[0].rhs()))],linestyle="--",color='black')
p+=line([(0,0), (sol1[0].rhs(),0)],linestyle="--",color='black')
show(p,aspect_ratio=1,axes=[False, False])#,transparent=True)

In the resulting plot, I would like to replace the portion of the horizontal axis between the yellow dot and the red dot by a horizontal dashed line. Is it possible?

Another question is how to display the values of the points on the axes.

Also, it seems there is no possibility to fill a polygon with a transparent color.

Another question: how to have the ticks in computer modern because two fonts is not nice.

And last but not least, I have seen that opacity is normally obtained by different words as opacity or alpha according to the context.