I have a a DLink DIR-803. Is there any maximum number of devices it can connect concurrently ? I can not find any information on this device online, while generic topic states there is no limit but I recently started feeling that net speed has reduced while more devices started using it.
Well without doing a bunch of crap you can assume 256 devices can connect (192.168.0.1 - 192.168.0.256) but realistically it depends on how good your router is.
There probably is a limit which depends on the wireless chip, but the real limit will be much lower. The more devices you have on a wireless network the more overhead and congestion you get. Unlike wired networks where every device can send and receive at the same time, on a wireless network only one device can send at any given time and all other devices have to wait. The network manages which device can send and for each device you have on the network the greater the overhead needed to manage that. Which means less available bandwidth for actual data.
Anyway, I'm not sure how many devices you can have before you get noticeable performance loss but you can probably look it up. But having more devices will definitely slow your network down. You can avoid this if you have a dual band WAP, and have some devices on the 2.4ghz channel and others on the 5ghz. Otherwise you could add another access point using a different channel and balance the load between them.
Theoretically.. 65535 per IP address configured on the router that a client can connect to. Realistically a lot less.
... Yes. 1 device potentially gets access to the full bandwidth, add another and it halves, add 2 more and it halves again.
Now yeah, that's not exactly true as it will depend on how the end devices are utilizing the bandwidth, some will use more than others. but the more devices you add assuming they use similar amounts of bandwidth the less you will have per device and the more time it will take to process as it has more than one connection to manage.