I added few competitors and checked their positions. Now, I want to do a search without their results, just my. Is there any options to do that, or I have to delete them? That is not an options because I will lose their results. Is that right?

Yes, the best you can do is hide them from display. Since Rank Tracker does not use any extra queries to get your competitors' rankings, you won't risk anything or lose anything. Competitors's ranks will be checked along with yours, but won't be displayed, so you can just go to Preferences -> Competitors and uncheck the "show competitors" checkbox.

Well the problem is that you cant add competitors in your project because if you do them everytime you check positions you check for them also.

So you need to have thousands of proxys and time.