Question: I have some questions regarding aforementioned subject:

* Is there a EC equivalent of RSA-OAEP key transport/encryption algorithm ?
* Is ECIES-KEM sufficient ?

Answer: 
Short answer, 
 - yes
 - yes
To be honest I don't really know how to give a longer answer. 
He are some pointers
<http://www.secg.org/download/aid-780/sec1-v2.pdf>
<http://digital.csic.es/bitstream/10261/32674/1/Gayoso_A%20Comparison%20of%20the%20Standardized%20Versions%20of%20ECIES.pdf>
As I understand it, there's really no RSA equivalent in EC. See, for example, [Why are elliptic curve variants of RSA "chiefly of academic interest"?](https://crypto.stackexchange.com/questions/3969/why-are-elliptic-curve-variants-of-rsa-chiefly-of-academic-interest)

Shoup's Integrated Encryption Scheme (ECIES) is an entirely different cryptosystem, and its probably closer to Abdalla, Bellare and Rogaway's [DHIES: An encryption scheme
based on the Diffie-Hellman Problem](http://charlotte.ucsd.edu/~mihir/papers/dhaes.pdf) in the integer world (sans the fact that ECIES is over EC).