So can someone tell me what this is. Is it an adjuster? Does it come apart to change out the cable? My cable pulled loose from the tension screw at the derailleur and I need to replace the inner cable. I need some advise.
Thanks for any help you can provide.

Yes it's an adjuster. You can just pull the cable through it without disassembling it. If for some reason you have trouble feeding the cable through it, you can just pull out the housing and feed it through one part at a time, then push the housing back in.

Do you actually need to replace the cable or just remount it?

You'll likely need to use that adjuster to add tension to the cable after reattaching it at the front derailleur. To give yourself as much tension adding capability as possible you'll want to screw the adjuster in as far as it will go before attaching the cable.

In being the direction that makes it shortest

It needs to be replaced. It's a new bike and it was hard to get the chain on the outer chain ring and p pushed the shifter pretty hard and it felt like the cable broke. Turns out it pulled loose from the retaining screw at the derailleur and due to that an me trying to get it back under the screw it frayed and has some broken strands. I hope the dealer will take care of it but if they don't I may attempted to fix it myself.

Can I remove the cable without taking the bar tape off? Will it just pull out if I cut the end off clean and pull it through from the shifter?

If it is a new bike, the dealer should replace the cable for you free of charge. If you didn't know what an inline cable is you probably shouldn't bet trying to change a cable yourself, if you mess things up you could void your warranty

I agree as it pulled loose for some reason but I don't think that was my fault as it wouldn't go up on the outside chain ring. I did more damage to the cable trying to get it back under the screw and adjusted. I will learn this stuff as I like to do my own work. That's why I joined the forum.

Well, the dealer replaced the cable today. I'm glad I didn't try to replace it myself as they had to pull the crank to replace the cable. The bike shifts much better than when I picked it up new Wednesday.

Sounds like it was internally routed and they forgot to feed a cable liner through when they pulled the cable. Having them fix it was the right call if you don't have any. Make sure that the rear shifts the same in the big ring and the small ring, sometimes cables get wrapped around in the downtube and pull on eachother.