Taking links out of a chain is a very temporary fix.... the issue with chain wear is that the bushings start to wear(people used to say that the chain stretches )when that happens the chain sits differently on the cassette . Removing links does not help this.... my theory is once you have problems fix it the correct way. There are all sorts of temporary things that you can do, but they are simply a band aid and generally don't last long. The problems by doing these temporary fix(s) become bigger and you tend to have more of them. If someone wants a bike to shift well in all gears, then the best solution is to replace the chain and cassette. Although with the sounds of this bike... as others have mentioned I would check cables/housing as well. We can talk these problems all day... but if you aren't able to do the repairs yourself then take the bike to your local LBS ... you'll feel much better when you can ride and you aren't thinking about the bike and its poor shifting.