The key to making cuts is to zoom in. In this example, you can see where the 2 tracks meet *blue circle) and "align". You simply can't see the alignment unless you zoom in. You can then see the thin lines on the sides of the arrow. You place the cursor over either one of those and then right-click to get the "Snip off" option. After you select it, you then select the piece you want to discard and delete it. If you did it right, they should automatically connect and the arrows should disappear.
NOTE: It works a little differently if you're on a grade because the heights might not match, but once you edit those, things should connect just fine.
In your layout, I had to snip the piece by the switch and then the short straight section coming out of the loop below that. Getting them both to line up was the hard part.
Now, when it comes to flextrack, you connect one end to one section of track to be joined. When you do that, you'll see the line I've circled in blue. You move that toward the other section of track to be joined until you get the red/green arrows. At that point, you right-click so the tracks connect and you get the 2nd photo. Sometimes, the angles won't line up to make the connection, so you have to right-click multiple times (blue circles) in different locations like I did in the 3rd photo to end up with what you see in the 4th photo. Notice the straight section that mimics what's in the design for your layout with the difference being only 2 joints instead of 4.
NOTE: You have to be very careful though to not "over" bend and end up with a radius your engines might not like.
