Yes and yes. At least, my DAR wanted them done before he showed up. You don't need a shop necessarily, but you do need someone with the right equipment.
My DAR just checked that my ELT was outputting, but I wasn't flying anywhere where I needed the transponder. However I was able to check it on the ground prior to first flight. I waited until out of phase 1 to have my pitot static certified by a repair shop. As far as I know that's only required before a?ny IFR flight.
I was referring to the pitot static certThe 24 month transponder rule IS required for VFR flight. (ref ? 91.413)
Another data point. The Reno FSDO requires pitot static check prior to their inspection. Dan from Reno
Another data point. The Reno FSDO requires pitot static check prior to their inspection. Dan from Reno