Ok thanks for all that Freethebee. Here's another attempt.

I've drawn E1 where it doesn't have the energy to tunnel, E2 where it does have the energy to tunnel and E3 where it is pretty much unaffected by the potential increase

For example, for E2 where it does not have the energy to tunnel, does it just look like what I have drawn for E1 but with a bit longer exponential decay to zero or does it have to cross the x axis and keep on decaying and end up having negative energy when it hits the infinite potential wall at a like I've drawn below?

Am I getting any closer to the right answers here or am I making any progress at all?

Here's another example of a well

Should the functions look anything like these attempts?

For 2 and 3 I've drawn the amplitude lower once it tunnels a bit into the barrier because the probability of finding it there gets lower but I'm not sure for 2 especially if functions are even allowed to decay in that direction?? i.e. upwards to zero

Thanks to anyone who is taking the time to look at my attempts.