1. You need to check here
http://www.immigration.govt.nz/opsmanual/46248.htm to see if your qualifications are exempt from assessment. If they are not, then you need to get IQA - one fee will cover both qualifications. (Don't bother with PAR, as you will need IQA for submission with the ITA at the stage after EOI, and in any case, it is not reliable.)
2. INZ will not accept anything in advance of the event, so you can't count two years' experience until you have completed them. (If you think about it, this is reasonable, because although you INTEND to work out the time, you could be prevented from doing it by unforeseen circumstances, such as illness, or redundancy.)
What you can usefully do in the meantime is get your evidence ready as far as possible. Think about police checks - they often hold people up, particularly anyone who needs one from the USA or certain Asian countries. You may also want to prepare your checklist of evidence to be supplied, updating it as more things occur to you. Many people do this in the order of items on the EOI form. It's useful to number the papers themselves, and note the numbers on the list, as well as a short description. This is making things as easy as possible for the CO, and (as long as you keep a copy) is useful for you - if the CO later emails, 'There is no evidence of your work for XYZ company,' you can reply, 'Yes. It is number 43 in my bundle, an A4 sheet on blue headed notepaper,' or whatever. Here are some old threads which may give you ideas to think over. Notice, the first post on the first thread has some things NOT to be done, and the explanation comes later.
http://www.enz.org/forum/showthread.php?t=44297
http://www.enz.org/forum/showthread.php?t=38818
http://www.enz.org/forum/showthread.php?t=21788
3. You need a separate letter from the university, specifically stating that you (name and date of birth) attended between whatever dates, studying for whatever qualification(s), and that the course was delivered entirely in English. The degree certificate itself is not sufficient for this purpose. If you can get such a letter, it should stand instead of IELTS, but notice that the CO working the case can require IELTS in case of any doubt. Also, many COs are so used to seeing IELTS as proof of English that their automatic reaction when they don't see it is to send out an email saying, 'Where is your IELTS?', but if you have mentioned in your covering letter and list of documents that your proof of English is a letter from XYZ University, it should be enough to reply drawing his/her attention to that.