For or a start see:
https://www.automaticwasher.org/cgi-bin/TD/TD-VIEWTHREAD.cgi?63898
1. Parts - can they be fixed? Who might be able to fix things? I'm not handy. Although, I am willing to try if I can find good instruction.
There are still persons around (Dave's Appliances, various Amish) who repair and or sell parts for at least Maytag and maybe SQ wringer washers. Who you can find locally might be another matter. Best to prepare for doing a bulk of work yourself, and or possibility of shipping washer great distance to someone that will do work.
2. Size - how heavy are they? Can they be moved easily? Do I need a buddy to haul?
Not very heavy at all. Both Maytag and SQ washers at least are easily moved in anything from a mini-fan to mid-sized SUV. What you want to do is keep washer upright to prevent oil from leaking. Despite its size the Maytag wringer glides across floor rather easily.
3. Materials - Is porcelain better than aluminium tubs?
Depends upon purposes. Aluminum is a soft and reactive metal. It will dull over time from contact with various chemicals commonly used in laundry (especially chlorine bleach), but can be buffed back to a nice state with a bit of elbow grease and patience. Maytag service men did this all time on units traded in to get them ready for resale.
Porcelain has advantage of being non reactive (and this includes using oxygen bleaches), and durable. But if it chips and underlying metal is exposed can lead to issues if not correctly promptly.
4. Longevity - Is it realistic to expect a few decades of use out of an old wringer, no matter how well it was kept?
Maytag wringer washers will (and in some cases have) lasted longer than their owners who died. This with doing many loads of washing per week for months/years on end.
Long as there are spare parts out there (and there is quite a lot) and proper maintenance is carried out, there is no reason why a Maytag wringer at least won't outlive yourself as well.
Of course much will depend upon state thing is in when acquired and age. If you can find a Maytag or even SQ from 1960's or 1970's (or later in case of Maytag) that saw little use, and was stored properly, again it just might outlive yourself.
5. Which one is better? The Speed Queen or the Maytag? The Maytag looks older but seems to be in repair. I have no idea about the Speed Queen's condition.
Maytag consistently was considered the Caddy of wringer washing machines. It outsold SQ and others by miles. But OTOH Speed Queen wringers had advantages such as deeper tub and some other bits many housewives found desirable.
Where Maytag shone was in durability. You literally cannot kill a Maytag wringer washer. This and their sales/service was top notch.
6. Price - what do wringer washers sell for at an estate auction?
It varies, and it all comes down to how much someone is willing to pay.
Recently a Maytag wringer sold on eBay for several hundred dollars. This while others have been sitting on same site for ages without even a nibble.
There are really tons of Maytag wringers out there, sadly when you want one chances are the good ones won't be nearby.....
7. Should I just wait it out and see if something better comes up?
That's it isn't it? Again Maytag wringers and even SQ models aren't exactly rare as some sellers would like to believe. Keep checking fleaPay, FB, Cl, Offer-up, etc....
Will say chances are better in scoring your dream washer if willing to travel and or pay to arrange shipping. This seems more true if live in a more rural area as opposed to urban location.
