Thank you for the information and your question. Whether or not the Company you are working for can let you go immediately, versus letting you work for the two week notice period depends entirely on whether or not the contract is a term contract. In other words, if you have a guaranteed job until XX date, and your two week notice takes you to that XX date, then the employer must let you work that period or pay you for the balance of the contract. On the other hand, if there is not term period and either party can terminate without cause, then unless the contract states that both parties must give two weeks notice, your employer could let you go right away. That said, there would be a valid argument to be made that if the contract required two weeks notice on your part, then it should also require that your employer do the same.
If this were an "at will
" situation with no contract, then the employer would not be required to let you serve out the two weeks and would not be required to pay you for that time. So, again, depends entirely on the language in your contract and whether it is a term contract or not.
As for your reason and where you are going, you would not be required to provide that information. If you have signed a non-compete agreement, they may want to know if you are accepting employment that will violate it, but you are not required to help them figure that out.
Please let me know if you need any clarification. I would be glad to assist you further if I can.