I have a beagle - an ex-working beagle.
All beagle will wander, they are scent hounds and they just can't help themselves. Dogs are particularly likely to do this and scent hounds are the worst.
I guess your is a KC reg. therefore he is likely to be more assertive than mine who was a pack dog.
Scratching the carpet in primeval instinct at work, this is the animal trying to make a bed for himself. Put him in a bed of straw and you would understand this. Mine does this all the time, and marks the carpet.
Beagles are very sociable animals and do hate being left. We put ours in a crate when we are out and it seems to offer her comfort now. She is happier to go into it, she will howl if we leave her out! She will always love a fuss and sometimes her attention seeking becomes wearing.
Our is also a faddy eater sometimes, she prefers anything that has dropped from the table or dd's hands to anything we give her.
They need loads of exercise, I have never come across a dog that trots around so much. Previous dogs have been happy to lie about in the evenings, not so with this one.
She is happiest when all of us are out walking with each other.
Mine also digs holes in the lawn which I can't stop no matter what I do. Theres no point in giving them chew sticks, they don't seem to understand them. However, you might find he likes wood.