As your prospective partner resides in her country of citizenship, you would not be able to join her there under the provisions of European Union law. You should therefore have a look at the IND page for spouse/partner visas.
Is there a certain monetary/income requirement for either of us?
To register your partnership, no. As an example, have a look at the requirements you'll need to meet if she resides in Amsterdam.
For you to get a residence permit in the Netherlands, yes (see below).
If I move out of EU, does the registered partnership allow me to visit & stay with her in the netherlands?
No. For stays of up to 90 days in any 180-day period, you will be able to visit with a normal short-term visit visa, also known as a type C Schengen visa. (Depending on your citizenship, you may not require a visa.) If you want to settle in the Netherlands with your partner, or even just visit for longer than you are allowed under the 90/180 rule, you'll need a long-term (type D) visa, which you will replace with a residence permit (citizens of a handful of countries are exempt from the visa but do need to get a residence permit). Requirements may be found at the page linked in the first paragraph. One of these requirements is that your partner have sufficient independent and sustainable income. The details, including the amounts, depend on your personal circumstances.
In case in future I want to work in the Netherlands, do I have to get a work permit?
Yes, but as the partner of a Dutch national, your residence permit will also permit you to work. You will not need an additional work permit (but you will not have permission to work in the Netherlands unless you move there and get a residence permit).
Are there any other things we need to be aware of for becoming registered partners?
There are probably many such things. You may want to talk to a lawyer. But the two pages linked above should cover all of the practical and administrative aspects of your question.
Finally, if the income or other requirements are burdensome, you should be aware that you can move instead to any other EU or EEA country under much more favorable terms: your partner only needs to be employed. After living there for some time (perhaps as short as six months), you would then be able to move back to the Netherlands under the same favorable terms.
