Your main issue here is that this is a very cheap iron so the quality of the tips corresponds as well.
Having said that, I started off with a similar soldering iron and never had that many issues. Here are some pointers/tips to troubleshoot the issues at hand.
1) Heat is too low. You want to be at least at 325 Celsius which equals to 617 Fahrenheit when soldering most components. The idea is to get in, heat up components/pads quickly, flow some solder, get out. This whole process should take no more than 5-8 seconds.
2) Never use abrasives such as sandpaper to clean soldering tips because that will remove the top layer quickly and render them useless. Use Steel Wire Mesh as well as Tip Tinner if you are having difficulties tinning the tips. Tips should be tinned before/in between use, as well as for storing.
3) That solder which comes with the kit is not very good; investing in something better will greatly improve your solder jobs and save you lots of headaches. Highly recommend getting Kester brand; it is available in 16 oz spools or smaller quantities.
4) Use flux freely when soldering. That solder paste in your picture should suffice. Make sure to clean it up afterwards with some Isopropyl Alcohol using a toothbrush and cotton swabs.
5) It would be useful to see (pictures) of what you were working on as well.
That is all I have for now.