I would say I don't see anything wrong with the cue you are currently using.
I would suggest using a nickel shaped tip with your 13mm shaft. You can get nickel tip shaping tools at billiards supply stores or online. A nickel shape is when you hold a nickel up to the side of the tip and the curve on the nickel matches the curve on the tip.
A differently curved tip will play differently. So if you were to get a new cue or a new tip which had a different curve (radius), it might play differently and cause your game to worsen.
It is good to always use the same brand and hardness of tip as well as radius (shape of tip).
Always playing with the same exact cue will go a long way to helping you become more consistent.
So far as improving your position play, get Dr. Dave's DVD at the following link.
(But you must practice every shot in the video. Diagram them, practice them, and understand them.)
http://www.engr.colostate.edu/~dga/pool/dvd_description.html
After understanding the above, ask youself where the cue ball will be going after each shot. Learn hot to get the cue ball to go where you want using the above.
Then speed control practice. Practice shooting just the cue ball 1/2 diamond, 1 diamond, 2. 3, etc. The to far rail and stop. Then to far rail and 1 diamond back. Etc. then to far rail an back to near rail (lag shot). Then plus 1 daimond, 2, 3, etc. All the way up to 3 rails.
Then break all 15 balls and practice shooting them so the balls roll just up to the pocket, but do not drop. This will teach you how slowly you can shoot shots (depending on if full ball hit or cut) and make the pocket - how slow you can shoot some shots and make the pocket. This helps if you don't want the cue ball to travel very far after the hit.
Then just practice this stuff daily. Also throw 3 balls on the table, mark their positions with chalk or stickers, then run them in leaving good position for each next shot. Do this again and again until you get it down, then try another. You can do a lot with the 30 and 90 degree rules shown on Dr. Dave's DVD along with follow, stop, and draw. I rarely use english myself.
Ask questions here about specific problems you are having. Over a period of years, your game will improve dramatically with the excellent advice given here.