Rec, overdub...

option for record notes (rec button), but without going to the initial position once the rec button is pressed??

No. 

(let's say I want to rec and overdub on the fly, while i'm looping a portion of the arrangement, without stopping and the cursor going to the initial position). 

Not possible. 

Also, when I press record, the loop markers disappears. 

Yup. Sucks. If you actually have some skills and want to real-time record, SF sucks big time.

I'm trying to punch in (with a footswitch) while recording in a looping section, without stopping the playback.

 Not possible.

Best,

tL.

Synfire's live recording features are indeed rather limited compared to a DAW. That's not because Cognitone was lazy, but due to logical constraints. What you are recording into is the Take parameter and what you're listening to is Figure rendered against Harmony and many other parameters. 

There is no direct link between input and output. For loop recording to work, Synfire would need to run figure recognition in real-time. That's pretty much impossible, at least today.

Also, since Take and final rendered output almost always differ, you would get lots of harmonic clashes during loop recording (unless you are accidentally playing exactly Synfire's output).

That's why recording is done in "shots" (or batches) rather than following the tape metaphor of a DAW.

For loop recording to work, Synfire would need to run figure recognition in real-time. That's pretty much impossible, at least today.

Impossible? Why? Let the notes record into a buffer while recording and commit to take

 only when pressing stop.  Kinda like a Guitar Looper... Don't see why that wouldn't be possible...

No need for Real-time Figure-Recognition at all....

Best,

tL.

The point of loop recording is to listen to what's there already, merged with what you have just recorded during last turn of the loop. Sort of adding new notes at every turn. For recorded input to be audible in the first place, the (partial) Take needs to be converted to Figure (unless you are comfortable with mixing up harmonically clashing snippets).

 Ah, I give up here. Now I am getting lectured about "the point" of looprecording... 

Adios.

Not lecturing anyone here (sorry if you got the impression). Just trying to explain why some DAW concepts don't translate well to a fully parametric context.