Few days ago I posted this problem https://www.vegascreativesoftware.info/us/forum/some-problem-with-cursor-clips-out-of-split-position-screenshot--111970/ on this forum. As title says, it has something to do with cursor & clips out of split position (link to screenshot - https://plus.google.com/u/0/photos/photo/115185730676100091884/6573931537499803906). Unfortunately, none of the given answers on that topic were right about the solution, still, thank you all who tried to help me (maybe it was my fail to explain well the situation, but at the moment, I just said what I thought it was necessary & has to do with the problem).
PROBLEM
So, as you can see through screenshot, I couldn't manage to put my cursor at split zone for some reason, even though I was able to do so when I split clips the first time, with NEVER TURNING OFF "Quantize to Frames". After creating new SV file, I pasted clips there from an old SV save file (old file that had no problems with that zone split cursor) & what I got ? The same problem with cursor out of split position. This gave me some clues to possible sources of this issue, as the old SV file had no problems with it, while new SV file had it. After a wasted hour of tries & searches in Sony Vegas Pro 13...
SOLUTION
This all problem with "cursor & clips out of split position" has all to do with PROJECT PROPRIETIES, namely, with FRAME RATE ! If you copy clips from one project (SV file), which is at "59,940 (Double NTSC)" Frame rate, & paste them to a new project but with a different frame rate, for example, "29,970 (NTSC)", you will get that problem with CURSOR PROBLEM (which is in that screenshot) !!! The only solution to it is to make both project files at the same frame rate !!!! In this case, it doesn't matter the resolution of projects, only the same frame rate. Take in notice that this ONLY MAY WORK if you first change frame rate at Project Proprieties & then paste clips - if you do the opposite (first pasted clips, then changed frame rate), it may not work.
I understand now that this might be a noobs issue & that all professionals knew this all the time, but I decided to post it since 1st- I couldn't find this solution on google, 2nd- I had no idea what key-words should I write in searches to find answers (wasted 30 minutes, with no results needed), 3rd- no right answer were given in my another post related to this issue (I assume it might me my fault of not giving more details - I just didn't know what was important to identify in that case).