@rokit .  Welcome to your first (mild) disagreement on this forum.  I do not think you purchased a cheap violin.  I think you got a very nice antique trade violin at an inexpensive price.  Big difference.

The worn area of the varnish is confined for an area which would normally be hidden by a chin rest.  This means to me that a previous owner did not use one and that facial hair or sweat wore away some finish.  No big deal.  I would gently clean off the surface with naphtha (lighter fluid) on a cotton undershirt and apply a coat of paste wax.  

Your tail piece gut appears to be made of actual gut.  I would upgrade that to a new one.  Wittner makes a wire cable one with adjustment screws that is worth the few dollars over the more common nylon versions.

That violin deserves the use of a piccolo style fine tuner on the “e” string.  A variant made of titanium is a worthy consideration.

My favourite violin bridge is marketed as “Cinderella” from China.  I would purchase 5 with the hope of making 2 good ones.  Look up my bridge roasting thread for additional fun.  

Other needs are chin rest, shoulder rest, strings, bow, and rosin.  Enjoy the journey.

The pegs look ok to me.  

Hi Gordon.  And that violin was built before the Chinese perfected a method of painting the figure in!  What impressed me was how close the grain was over the center of the spruce front plate.  

@rokit .  If you have access to bungee cord, I would make a retainer with it to slightly compress the center of the violin corpus, thus retaining the sound post as you work on the violin.

String selection is slightly premature because you do not know how high the bridge is going to be at this point.  If the bridge does not need to be radically reduced, violin strings with a perlon core would be a good choice.  The fiddlerman store brand is not too expensive in the United States and they play well.  This cost may be off set from over seas shipping and duty.  

If you need to cut off a lot of bridge due to neck angle or corpus carving profile, you may need to go with steel core strings to achieve a good sound volume.  Typically, this type of string cost about 1/3 of that of a perlon core string.  

@rokit .  If you have access to spruce, pigment (water colours, oil paint, or leather dye), woodworking tools, woodworking glue, and shellac, go for the repair.  No further harm will be done to the violin if left alone.  Damage will have no acoustic significance.

I do not know the climatic conditions of your regions.  You may want to add a humidifier to the case.  I posted an easy diy humidifier in another tread here.

@rokit .  Another thought.  After a second view of your provided photos.  It appears to me that the ebony wood saddle is shorter on the side of tailpiece than the opposite side.  I think the exposed wood is due to a chip breaking off the original saddle.  If so, it would be a rather easy matter to replace the saddle (equally easy to do so if they are currently equal).  

@rokit .  The old saddle is likely held on with hide glue.  It is tenacious at room temperature but returns to a liquid at about 100 c.  Find something similar to a very thin butter knife (with no sharp edges), heat blade with an electric hot iron or similar and gradually introduce blade under the saddle.  

The new ebony saddle is likely to be oversized.  When machined to match old, apply a little acetone to underside before application of glue to remove wood oils.  That makes it secure better.  White wood glue would work fine, since the tail piece gut is acting on it in compression.