You have asked several questions here that might require answers from both an attorney and a landscape architect or engineer, depending on how much of a nuisance this potential flooding and plant/animal incursion is, its threat of occurance, the cost/benefits of paying consultants, and whether this is a serious potential problem for you or just an annoyance and you don't like the Town telling you what to do.
As to the fence location: if it was there for 30 years in the same place, it has probably extinguished any former easement or claim of ownership that exists "on paper" through the magic of "adverse possession". There is also the legal issue of whether this Town requirement is a voluntary suggestion of a planner or building inspector or a binding legal obligation as part of the conditions for geting the variance you mentioned. If the latter, it will be much harder to avoid the requirement and you may have to go back to the ZBA to abolish it. Prepare to have justifiable reasons, and perhaps to let the engineer or LA "front for you" before the Board with your concerns.
Lastly, as to the probability of the nuisance you forsee, the severity and whether other measures may be taken to mitigate it or avoid it while still having the fence the way you like it, consult with an engineer or LA. The problem could be solveable with a swale or stone lined ditch or pipe in the right place.
This answer is provided under the Avvo.com “Terms and Conditions of Use” (“ToU”), particularly ¶9 which states that any information provided is not intended as legal advice or to create an attorney-client relationship between you and me or any other attorney. Such information is intended for general informational purposes only and should be used only as a starting point for addressing your legal issues. In particular, my answers and those of others are not a substitute for an in-person or telephone consultation with an attorney licensed to practice in your jurisdiction about your specific legal issue, and you should not rely solely upon Legal Information you obtain from this website or other resources which may be linked to an answer for informational purposes. You understand that questions and answers or other postings to the Site are not confidential and are not subject to attorney-client privilege. The full Avvo ToU are set forth at http://www.avvo.com/support/terms . In addition, while similar legal principles often apply in many states, I am only licensed to practice in the State of New York and Federal Courts. Any general information I provide about non-New York laws should be checked with an attorney licensed to practice in your State. Lastly, New York State Court rules (22 NYCRR Part 1200, Rule 7.1) also require me to inform you that my answers and attorney profile posted on the Avvo.com site may be considered "attorney advertising" and that "prior results do not guarantee a similar outcome".
Just to briefly add to what Mr. Lebowitz said, it would be a good idea to go to the township and to review any information they have regarding the alleged easement, as well as any zoning or planning board resolutions affecting that property and your property. The towship might be "requesting" you do certain things, but there you may have no legal obligation to actually do it. Also, as Mr. Lebowitz noted, the legal concept of "adverse possession" may come into play. To oversimplify, this is a situation where one person, because of their unbroken and public use of a parcel of land over a period of time, actually becomes the owner of that property. If you are deemed the owner of the easement, the town may not be able to enforce ANY of the easement provisions. You should consult with an attorney to find out more information.
If you think this post was helpful, please check the "good answer" button below! NOTE: This answer is made is for advisory and/or educational purposes only. By using or participating in this site, or posting a question and obtaining an answer, you understand that no attorney-client relationship is being established between you and the answering attorney, and there is no attorney-client privilege between you and the attorney. You should consult with a licensed professional attorney in your state. The law changes frequently and varies from state to state. The information provided in this answer is designed to be general in nature and is based on the facts stated in your question, and might change based on further information.
Part of this is going to depend on what you mean by "easement area." If the easement is owned by the Township, then the Township may have more control over this situation than otherwise. Generally, you cannot adversely possess or take over property owned (even in part like an easement) by a governmental entity. Also applicable are the local building/planning requirements for a fence of this type. As both other commenting attorneys have properly advized the Township has a variety of powers in this situation depending on the ownership of the easement and the building/planning requirements. You may need to retain an attorney to work through these details, or at a minimum ask the Township representative to sit down with you and explain its authority for what is being requested. Finally, even if the Township has the right to control the fencing in the manner they are, you may still have a claim against them if the water and invasive plants and animals to your property are a problem being created by the Township. However, as to this later issue you would certainly need to retain an attorney to determine if you even have a claim based on the facts of your situation.