Starting with the warnings concerning weak security, or other elements of your WiFi setup, your WiFi network may benefit from update in either settings or improved hardware...
Your iPad is no less secure today than it was prior to the update to iPadOS14. However, your iPad is now better able to [warn] bring to your attention security deficiencies of your WiFi network and iPad settings.
This support page will describe the more secure (recommended) settings for WiFi:
Recommended settings for Wi-Fi routers and access points – Apple Support
It is possible that your WiFi Router is too old to be (or not capable of being) configured for more secure settings. As such, you can either configure the most secure settings that your Router will support - or replace your Router with something more advanced that provides better security configuration options.
Whilst WPA3 is the newest standard, you should aim to use WPA2 (AES-PSK) as a minimum. Some Routers seemingly continue to support the insecure/deprecated TKIP standards - even when apparently configured for WPA2 operation; TKIP will definitely cause a security warning to appear. Be aware that if you are using a WiFi network extender, these may continue to use weaker security standards - and continue to trigger a warning.
There is a also new privacy feature included within iOS/iPadOS14 that hides your physical MAC Address - and instead uses a randomly selected Private MAC Address. This feature can be enabled/disabled on your iPhone/iPad for each configured WiFi Network. This feature also has bearing upon the appearance of the Weak Security notifications.
More information about this new feature can be found here:
Use private Wi-Fi addresses in iOS 14, iPadOS 14 and watchOS 7 – Apple Support
If you are unable to employ more secure security settings on your WiFi network, you might consider replacement of your WiFi network equipment, such as your WiFi Router, with more advanced equipment. However, if the router is provided by your ISP, this may not be practical proposition. A potentially cheaper and more flexible approach might be to add an additional upstream WiFi Router, of WiFi Access Point (AP) that meets the required standards.
Now, to address your issue with client devices attempting to connect to your neighbours WiFi network. This can only occur if:
a) both WiFi networks are using the same Network Name (SSID); separate WiFi networks must be configured with a unique Network Name / SSID, or
b) you have configured your iPad to attempt connection to another WiFi network; either Forget the WiFi network that you do not wish to connect from your iPad, or disable the Auto-Join setting for this network. Tap the “i” icon adjacent to the WiFi Network name to access these options.
Connect to Wi-Fi on your iPhone, iPad or iPod touch – Apple Support
I hope this information provides some helpful insight into ways to resolve the WiFi Security warnings.
