1) The key configuration requirement is the no of tube side passes for this application. You can only use one tube side pass for this case. For type E shell side pass, use only one tube side pass in counter current configuration. You can wire up as many shells as you need (if one shell does not suffice), provided they are all wired up in series on both shellside and tubeside, and the flow arrangement is countercurrent for all shells.
For type H shell, it is a little more complicated. Compute the F factor - see Fig 11-4 on page 11-6 of Perry Chem Engg Handbook in the chapter on Heat Transfer Equipment Design. R = 1.0, S = 1.0. See fig h - the F factor for R = 1.0 and S = 1.0 is less than 0.2. So you cannot make this work with H type shell, even if you have a single tube side pass ,since F < 0.2 - you need a min value of F =0.75 to 0.8 to make it work.
2)A plate HE can be used for this application provided it is 100 % countercurrent flow
3)Am familiar with these terms, but to my knowledge, these terms are too loosely used by process engineers, so I'd rather not comment. But I can say that no HE, shell and tube or plate type, can get you around a internal temp pinch. Whether or not this application involves a temp cross depends on the configuration. For a pure countercurrent configuration, there is no cross. If you were to use 2 or more tube side passes or a type H shell or similar, there would be an unworkable internal temp cross (or pinch).