Don't ever use manure and that looks like carrot root fly damage.

I can answer the second part of the question - the carrot and pen appear to be horizontal with the root and the point on the right, but can't tell whether this is what you intended!
I can't grow carrots either. If the ever germinate they disappear after a couple of days, so I tried in deep pots of compost - they did grow a bit in there but the carrots weren't worth bothering with and the slugs found them even there. I buy mine and grow something else as it isn't worth the hassle for me.

Carrots grow best in a light, sandy soil with a fine tilth. So, no manure or rooster booster! You will probably also have to net them to keep the root fly out.

Many thanks people, I'll get some sharp sand, mix it with say 50% sieved soil which I already have without manure etc added ) and put it in a tub this time and try again.
I mean to succeed eventually.

Then forget the above and do this.
Get horticultural sand and bagged top soil. Mix 1:1.
Use any spare multipurpose compost you have left over, sieve it, and mix it 1:1 with the above.
If you haven't any spare, buy any peat based compost or plain peat, sieve and use as above.
Fertilise with vitax q4 powdered fertiliser.
Quantities depend on how big your container is.

I saw on tv that if you plant some herbs near the carrots the carrot fly can't smell them. Don't know if this works or not, but may be worth a try or looking up. And water regularly if on light sandy soil. Good luck.

Thanks Scrumpy, I'll do exactly as you say. And the herb tip looks good too.