Anyone know if the Yongnuo YN-560 II Speedlight Flash is suitable for use with a Nikon D3500 been offered on at a good price
A YN-560 II could be a suitable flash for off-camera use, Strobist-style, but it's cheap for a reason: it's 3rd-party Chineses manufacture, and it's an older model. It's been superseded by the YN-560 III, the YN-560 IV, the YN-660, and YN-560Li models, and most of us prefer Godox these days to Yongnuo for expansion options. Unlike its younger brothers, the YN-560 II has no built-in radio triggering or remote power/zoom control.
For on-camera use, particularly if you're event shooting and won't have the time to constantly be adjusting power, it's not particularly suitable. The other reason it's so cheap is that it's system-agnostic, single-pin, and manual-only (ditto the Amazon Basics flash and the Neewer TT560, both of which, I suspect are a rebranded Godox TT560). The only thing a camera hotshoe can tell the flash is when to fire. There's no TTL (automated power setting based on metering), no HSS (high-speed sync), or camera menu communication, as there would be with a more expensive iTTL-capable flash for a Nikon camera.
I would recommend budgeting between $100-$200 for a first/only flash purchase, and say look at either a used SB-600/700/800/900, or a Godox TT685-N (at this time; flash tech moves fast in the cheap Chinese manufacturing sphere—this recommendation could be quickly outdated). The Nikon will be better for on-camera use; the Godox for off-camera use, so how you intend to use the flash can have a lot to do with what flash is right for you.
It is a manual flash with one single pin, so yes it will work on camera.
But In my opinion, the best way to use a flash is off-camera, so you can still use it in many ways.
You could buy an external transmitter and receiver. There are some brands really cheap, or the same brand, like the RF-603.
If you later decide to get some with a built-in receiver, you still can use it as an optical slave.
Additional flashes are a good thing, for example when illuminating large areas, a big ballroom, etc. But the optical slave has limitations in range and versatility.
Personally, I can not live without radio triggered flashes anymore. :o)
Some transmitters can change the power output, turn them off, etc. So the versatility you get used to is a must.
But it still works.