Rolling is only really effective for frost heave and small bumps. The only way to smoth an areas to remove large humps (or swails as depicted in your photo) is mechanical (box blade to move excess from the humps and redeposit in the dips) or 2. add soil/sand to the dips and raise to the top of the humps.
Use of a roller on wet soil (when the soil is most susceptable to deformation) will remove the spaces in the soil which will reduce the ability of water and air to penetrate. Use of a core aerator will remove plugs of soil and as they desolve the water will carry them to low areas. This may help to smooth the lawn over years.

thanks for that grass1950

I have never used an aerator. How often should a lawn be aerated?

Also, do you think the low end aerators (~$200 buy) are worth it, do they work? Or just go rent one ($80/day including deliver/pickup). Local rental place has a tow-behind BlueBird 48".

Let me clarify that I am not recommending core aerification for smoothing a lawn. The amount of soil that would be moved from high areas to low would be a "spit in the ocean", even if you raked the cores from the high points to the low areas for years. I was surmizing that it may have more effect than rolling which is going to have no effect on large bumps/swails. At least not in my experience.
In my opinion and experience, core aerification can serve some useful purposes. It allows air, water and nutrients into the soil. Consequently, It can improve root mass. It can help drainage in wet areas. When combined with topdressing, it can allow Om and and ammendments like gypsum to reach further into the soil. It is considered an aid when combined with overseeding--but debateable.
One of the major knocks/concerns of opponents is weed preasure as they claim core aerification will bring up weed seed and spread poa annua and triv. (I have never had any increase in weed problems)
Like any process, it should be employed to address an identifiable purpose and continued only if there are results. Not just for the sake of doing it.
To your questions:
University turf programs recommend core aerification every one to three years as needed. Aerification should be done in the spring before application of a pre-m or in the fall a couple of weeks before dormancy so the turf has time to spread and recover. I do both (in fact, I have aerified uo to 4 times in a year) and do it every year, I also combine it with topdressing/gypsum as I need to improve OM and tilth.
The homeowner's $200 model by Binley, Agri-fab or Craftsman is just that, a homeowners model. They are not heavy duty and will not take heavy abuse. If run at slower speeds, they can last for years. (I have had a Brinley for four years and have had no issues. It's as solid as the day it was bought except for some to be expected wear of the tines. Unlike your 4 ac. I only have under a half acre- closer to 1/3 actually.) These models have fewer tines than professional units and will result in around 4-5 cores per sq ft per pass-so multiple passes will be needed to get the recommended 12-20 cores per sq ft..
The Bluebird is a professional purpose aerator (Ryan makes a simular model) and will operate at moderately higher speeds..They have more tines per spoke assembly and consequently will result in more cores per sq ft per pass ( I believe it is 8-9)
If you wish to try core aerification, I suggest you pick up a barely used homeowner's model off craiq's list. They are commonly sold for $50-$100. About the cost of rental of the Bluebird. If you decide that the results are such that you are going to want to implement aerification regularly in the future, you can find used Bluebirds or Ryan pull behinds (which you should consider for your large lawn) on CL too . I recently saw a Bluebird in my area for $300 (admittedly, that is an unusually low price, but bargains can be found.).