plot(1:10)
1.:
set(gca,'FontSize',14)
3.:
box off
2.: You have to create subplots manually, for example:
axes('Units','Normalized','Position',[.1 .1 .1 .1])
axes('Units','Normalized','Position',[.2 .2 .3 .1])
axes('Units','Normalized','Position',[.5 .3 .3 .1])
4.: In my opinion there is no property like 'AxesThickness', but you can add lines to your plot to 'simulate' it:
plot(1:10)
x = get(gca,'xlim');
y = get(gca,'ylim');
line(x,y([1 1]),'Color','k','LineWidth',3)
line(x([1 1]),y,'Color','k','LineWidth',3)
box off