There's several possible kinds of issues:
There are antiviruses that report Tox as false positive. If you did get Tox from official Tox website, and your antivirus causes problems and is not in the list please say that antivirus causes problems. Additionally, you could report to your antivirus makers that Tox is reported as false positive when it should not be.
Unfortunately, current Tox groupchats don't support saving, moderation or joining without invite. The New groupchats, which are still in development, will fix these issues.
Some routers go offline when using Tox, as they incorrectly track UDP packets sent to an ip/port as an individual connection, eventually hitting a connection limit and disconnecting. This is partially a core issue, and work is being done to mitigate its effect. In the meantime, there is a workaround - disable UDP in your Tox client, as this will reduce the number of connections tracked by the router.
Tox messaging of all kinds requires both parties to be online at the time the exchange takes place. Some clients implement pseudo-offline messages, where they save a message and schedule it for delivery the next time you and your friend are both online. This is safe, but it still requires both parties to be online. The developers are working on an implementation of offline messaging which works without compromising the security, privacy, and decentralization that Tox promises.
If you use a client which allows you to schedule pseudo-offline messages, in order for them to be delivered you have to both be online. If you are the person who scheduled the message, staying online at your computer will help maximize the chance you will be online at the same time as the intended recipient, but leaving your computer or device unattended with messages visible on the screen is a potential security risk to somebody who just happens to walk by.
Tox messaging of all kinds (including Friend Requests) requires both parties to be online at the time the exchange takes place. Try to make sure that both computers are connected to the network when the friend requests are made.
In order for a friend request to complete:
If you are sure that other side was online when you sent the Friend Request, and they did not receive it, please report it.