There are of course more but I'm trying to figure out how would I even solve this first one in order to do the rest. Any hints or help in the steps would be appreciated. I'm literally out of ideas.
The only chance you have here is either:
show that it is not preimage-resistant, i.e. how you could, given a value $h$ find a preimage $(x,y)$ with $H(x,y) = h$. Using the structure of the hash-function might help here.
reduce the preimage-resistance to some property of its constituents, here the block cipher. So, show that if you have some machine (function) $\tilde H_1$ which, for an input $h$ gives you a preimage $(x,y) = \tilde H_1(h)$ with $H_1(x,y) = h$, you can construct a machine which violates some of the properties of an ideal block cipher (like allowing to find a key or plaintext from ciphertext, or something similar – look for your definition of ideal block cipher). (This likely won't work for $H_1$, but might work for some of the other ones.)
For all of the non-broken real-world hash functions, unfortunately we can't do any of those, because we don't have ideal ciphers.
$H_1 (x,y) = E_y(y) \oplus x$
$H_1( E_y(y) \oplus x ,y)= ?$
$H_1( E_y(y) \oplus x ,y)= E_y(y) \oplus E_y(y) \oplus x = x$