Could you provide a a couple of examples of channels which are missing?
You may find your new TV has a lower tolerance to interference, and your new Samsung TV will not channels with poor\low signal. Freeview have a list of suggestions which can be found here.
To start with I would perform a factory reset of the TV to clear all settings, check the coax cable is undamaged and connected firmly into the TV and wall, then re-tune.
If the channels still do not reappear, I would consider investigating the signal strength (which may impacted by a poor coax cable, poor quality aerial or incorrectly installed aerial).Looking at how the 3 channels you are watching are broadcast More4 and Film4 are part of the same group as ITV and Channel4, so would tune into ITV2 for example, then look at the TV's signal strength, as see if adjusting the aerial improves this, before then doing a further re-tune.
You can access the channels signal strength by selecting the channels, pressing the "D.Menu" button on the remote, selecting "Setup", then "System" followed by "Signal Information" from the on screen displays. You may then wish to compare this to another channel such as BBC.
Should you need anything clarified please let me know.
You wont be able to tune to 14, you should tune to ITV or Channel 4 (channel 3 or 4), and pull up the signal strength.
BBC should have a higher signal strength as that is on a separate transmission bandwidth.
Let me know what the difference is between BBC, ITV and Channel 4, there should be a strength and error rate value.
What options do you see when you push the menu button?
The clicking noise will just be the relays turning on (nothing to be concerned with).
So you tune to BBC 2 for example, on the remote you press "d.Menu" and then get options for the TV guide, your not seeing a menu such as the one attached?
On the left hand side of the screen are there icons, if so can you see one which looks like a cog (similiar to that in the image)
In Setup, scroll down, are there any other options past Audio PCM (there should be additional options \ second page)?
If not it sounds like you have a different firmware version, and ill find out where the signal information is hiding, sorry this is taking longer than I had hoped.