yes on the former, not sure on the latter and depends whether it is direct wiring or a plug, the latter no, the former would be recommended to go that route.....
If the gas hob has a "bayonet" connection......... you can do it yourself. A bayonet is a "plug & socket" arrangement.
If you don't have this, so a permanent connection has to be made, then this must be done by a Gas-Safe guy.
You may disconnect an oven electrically where the cable enters the oven. You are then allowed to connect this into the new oven.