You might, there is a LINE OUT jack on the CD player. You need to get an AC/DC power adapter - not supplied with the CD. Plug one end of the power cable into the CD/AUX jack in the car.
Most new cars will have an auxiliary input for their sound system. If the auxiliary input accepts the small plug for headphones, then you can plug into that with a cord that runs from the headphones output on the external CD player. This CD player has that option. I do this on my newer car and it works fine.
Not sure of what you mean by a low level output connection, but there is a connection next to the "PHONES" connection that says "LINE OUT." That probably can be connected to a small speaker. There is a DC IN 4.5 V jack, but there doesn't appear to be an AC adapter connection. You might want to consider asking someone at Best Buy if there is an adapter available.
You can find details Specifications in the User Manual, downloadable via http://www.insigniaproducts.com/products/portable-audio-players/NS-P5113.html?supportTab=open.
It has a HOLD button, but it won't keep the CD track in place. The HOLD button is so that tyou don't waste batteries by inadvertently turning on the player when you didn't mean to.