As a fairly new NCO, am I supposed to give my soldiers initial and monthly counsellings (PSG is asking for monthly)?

SGM Douglas Vidakovich pretty much sums it up. It is a lost art and sadly this is why so many are able to continue, when they shouldn't, and why so many great guys don't get promoted. I would add though that it's also a great tool to ensure the senior rater knows how your guys or gals are doing. So find out what their senior rater perceives their strengths and weaknesses are and then help them work on those. Set them up so the senior rater can see them performing at a training event etc. Help the good ones up and the bad ones out.

Boy we sure didn’t get that much counseling when i was in. But then it was the Navy, pretty much stand alone

For the same month

Counseling statements were always monthly, and then of course also driven by events in between the monthly counseling period. Hint: The event driven doesn't always have to be negative. Yes, if Joe has a habit of being late to formation, that's worthy of a written counseling but so can particularly noteworthy performance.

Monthly counseling...yes. From my experience, since I was never given a counseling report, until I f*** up, it became a chore, when I became an NCO. My advice; don't wait until your Platoon Sergeant gets an attitude with you. Be honest, if you don't know how to do one, let him know, so he can train you, or get someone to train you. It takes training and practice to do those reports. Just because you put on the Sergeant stripes for the first time, doesn’t mean you automatically know everything.

Yes and yes. Initial counseling so your soldiers know what is expected of them by you and the rest of their CoC, and for you to hold them to that standard and grounds to counsel them if they don’t. The monthly is so both you, the soldier, and the CoC can track their goals, development, and training, as well as leaving a paper trail for “challenging” soldiers should it be necessary. It also allows you to see if a soldier deserves special recognition or early advancement etc in relation to their peers.
Check out TC 7-22.7 and AR 600-20 for guidance, and don’t hesitate to ask your NCO support channel for mentoring; that’s part of their responsibilities as a leader as well.

Or if you have NCO below you they do them and you council them

Duh

As an E-3 we want to know how we are performing, what we need to work on, and we need the input from senior enlisted. Without that you get a platoon of people who don't know what they are doing, where they are lacking, and generally don't give a damn about being there. That's how you end up with NCOs that don't need to wear their rank.

Counseling your shoulders let's them know where they stand, if they're doing a good job, or if they need to improve on things. Kind of like in the medical field, if you didn't document it did it really happen? By doing this it's a paper trail for both you and your soldier. If you want to put your shoulder in for an award you have documentation backing you up as to why they deserve it, video versa if you need to reprimand them you can show why this is needed. This can be helpful not only for your lower enlisted, but NCOs that fall under you as well, that way when they go to fill out their support form they can look at their counselings for thing they may have done.