You seem to be describing three unrelated issues.
The first, relating to your home WiFi Router, you provide few details. It is impossible to provide specific guidance as many factors can impact WiFi connectivity - including but not limited to your Router’s WiFi settings, the WiFi band (either 2.4GHz or 5GHz), local WiFi signal interference (such as fluorescent lights, microwave ovens etc.). As described, you are able to connect to the network.
Your second issue - most “free” WiFi networks are insecure by definition, as they are “open” networks that do not use encryption. Your iPad will display a warning whenever you attempt to connect to a network where your security and/or privacy are not assured.
Lastly, you provide no insight as to the source of the books that you are attempting to download - or their particular format (such as ePub, PDF or something else). Documents/books that you download will not necessarily be automatically associated - or be compatible with - the native Books App. If you can provide more details, it may be possible to provide appropriate guidance.